Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D199 |
| commutator, socle, cosocle | C22×C199 | C24 |
| Frattini | C22 | C23×D199 |
| Fitting | C4×D4×C199 | C2 |
| hypercenter | C4×D4 | D199 |
| hypocenter | C199 | #525 |
| LCS | G ▷ C22×C199 ▷ C199 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15691886 | C2 | semidirect |
| 2. C22×C4×D199 | C2 | semidirect |
| 3. #20263940 | C2 | semidirect |
| 4. #20263937 | C2 | semidirect |
| 5. #20263933 | C2 | semidirect |
| 6. #20263932 | C2 | semidirect |
| 7. #20263928 | C2 | semidirect |
| 8. #20263927 | C2 | semidirect |
| 9. #20263925 | C2 | semidirect |
| 10. #20263923 | C2 | semidirect |
| 11. C4×D796 | C2 | semidirect |
| 12. C4×C22⋊D199 | C2 | semidirect |
| 13. C4×C22⋊D199 | C2 | semidirect |
| 14. #20263912 | C2 | semidirect |
| 15. C4×D4×C199 | C2 | semidirect |
| 18. C2×Dic398 | C22 | semidirect |
| 24. C2×C22⋊D199 | C22 | semidirect |
| 31. C2×C4×D199 | C22 | semidirect |
| 32. C4⋊Dic199 | C22 | semidirect |
| 33. Dic199⋊C4 | C22 | semidirect |
| 34. Dic199⋊C4 | C22 | semidirect |
| 35. Dic199⋊C4 | C22 | semidirect |
| 36. Dic199⋊C4 | C22 | semidirect |
| 38. C22⋊Dic199 | C22 | semidirect |
| 43. (C2×D199)⋊C4 | C22 | semidirect |
| 44. (C2×D199)⋊C4 | C22 | semidirect |
| 45. C4×Dic199 | C22 | semidirect |
| 48. C22×C4×C199 | C22 | semidirect |
| 49. C4⋊C4×C199 | C22 | semidirect |
| 51. C22⋊C4×C199 | C22 | semidirect |
| 52. C42×C199 | C22 | semidirect |
| 76. C4×D199 | D4 | semidirect |
| 92. C22×C199 | #41 | semidirect |
| 103. C2×D199 | #41 | semidirect |
| 122. C199 | #525 | semidirect |
| 137. C4×D4 | D199 | semidirect |
| 157. C22×C4 | C2×D199 | semidirect |
| 163. C4⋊C4 | C2×D199 | semidirect |
| 173. C22⋊C4 | C2×D199 | semidirect |
| 175. C42 | C2×D199 | semidirect |
| 225. C22 | #15691886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691886 | 2 |
| C22×C4×D199 | 2 |
| #20263940 | 2 |
| #20263937 | 2 |
| #20263933 | 2 |
| #20263932 | 2 |
| #20263928 | 2 |
| #20263927 | 2 |
| #20263925 | 2 |
| #20263923 | 2 |
| C4×D796 | 2 |
| C4×C22⋊D199 | 2 |
| #20263912 | 2 |
| C4×D4×C199 | 2 |
| #525 | 199 |