Finite Group DatabasebetaFinite Group DatabasebetaOrder 12352.
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×D193 |
| commutator, socle, cosocle | C22×C193 | C24 |
| Frattini | C22 | C23×D193 |
| Fitting | C4×D4×C193 | C2 |
| hypercenter | C4×D4 | D193 |
| hypocenter | C193 | #525 |
| LCS | G ▷ C22×C193 ▷ C193 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15690555 | C2 | semidirect |
| 2. C22×C4×D193 | C2 | semidirect |
| 3. #20259884 | C2 | semidirect |
| 4. #20259881 | C2 | semidirect |
| 5. #20259877 | C2 | semidirect |
| 6. #20259876 | C2 | semidirect |
| 7. #20259872 | C2 | semidirect |
| 8. #20259871 | C2 | semidirect |
| 9. #20259869 | C2 | semidirect |
| 10. #20259867 | C2 | semidirect |
| 11. C4×D772 | C2 | semidirect |
| 12. C4×C22⋊D193 | C2 | semidirect |
| 13. C4×C22⋊D193 | C2 | semidirect |
| 14. #20259856 | C2 | semidirect |
| 15. C4×D4×C193 | C2 | semidirect |
| 18. C2×Dic386 | C22 | semidirect |
| 24. C2×C22⋊D193 | C22 | semidirect |
| 31. C2×C4×D193 | C22 | semidirect |
| 32. C4⋊Dic193 | C22 | semidirect |
| 33. #15690534 | C22 | semidirect |
| 34. #15690534 | C22 | semidirect |
| 35. #15690534 | C22 | semidirect |
| 36. #15690534 | C22 | semidirect |
| 38. C22⋊Dic193 | C22 | semidirect |
| 43. #15690532 | C22 | semidirect |
| 44. #15690532 | C22 | semidirect |
| 45. C4×Dic193 | C22 | semidirect |
| 48. C22×C4×C193 | C22 | semidirect |
| 49. C4⋊C4×C193 | C22 | semidirect |
| 51. C22⋊C4×C193 | C22 | semidirect |
| 52. C42×C193 | C22 | semidirect |
| 76. C4×D193 | D4 | semidirect |
| 92. C22×C193 | #41 | semidirect |
| 103. C2×D193 | #41 | semidirect |
| 122. C193 | #525 | semidirect |
| 137. C4×D4 | D193 | semidirect |
| 157. C22×C4 | C2×D193 | semidirect |
| 163. C4⋊C4 | C2×D193 | semidirect |
| 173. C22⋊C4 | C2×D193 | semidirect |
| 175. C42 | C2×D193 | semidirect |
| 225. C22 | #15690555 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690555 | 2 |
| C22×C4×D193 | 2 |
| #20259884 | 2 |
| #20259881 | 2 |
| #20259877 | 2 |
| #20259876 | 2 |
| #20259872 | 2 |
| #20259871 | 2 |
| #20259869 | 2 |
| #20259867 | 2 |
| C4×D772 | 2 |
| C4×C22⋊D193 | 2 |
| #20259856 | 2 |
| C4×D4×C193 | 2 |
| #525 | 193 |