Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
310 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×Dic398 | C2 | semidirect |
| 3. #20263920 | C2 | semidirect |
| 4. D4×Dic199 | C2 | semidirect |
| 5. C4×C22⋊D199 | C2 | semidirect |
| 6. (C22⋊D199)⋊C4 | C2 | semidirect |
| 7. #20263913 | C2 | semidirect |
| 8. #20263911 | C2 | semidirect |
| 9. C2×C4×Dic199 | C2 | semidirect |
| 10. C42×D199 | C2 | semidirect |
| 11. C4×D4×C199 | C2 | semidirect |
| 12. #15691885 | C4 | direct (N × H) |
| 37. Dic398 | C2×C4 | semidirect |
| 38. C22⋊D199 | C2×C4 | semidirect |
| 40. C2×Dic199 | C2×C4 | semidirect |
| 48. C4×D199 | C2×C4 | semidirect |
| 50. D4×C199 | C2×C4 | semidirect |
| 66. C4×C199 | #41 | semidirect |
| 71. Dic199 | #41 | semidirect |
| 77. C199 | C4×#41 | semidirect |
| 85. C4×D4 | D199 | semidirect |
| 118. D4 | C4×D199 | semidirect |
| 149. C4 | #15691885 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691885 | 2 |
| C4×Dic398 | 2 |
| #20263920 | 2 |
| D4×Dic199 | 2 |
| C4×C22⋊D199 | 2 |
| (C22⋊D199)⋊C4 | 2 |
| #20263913 | 2 |
| #20263911 | 2 |
| C2×C4×Dic199 | 2 |
| C42×D199 | 2 |
| C4×D4×C199 | 2 |
| C4×#41 | 199 |