Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. #14271976 | C2 | semidirect |
| 2. #14271972 | C2 | semidirect |
| 3. #14271968 | C2 | semidirect |
| 4. #14271548 | C2 | semidirect |
| 5. #14271434 | C2 | semidirect |
| 6. #14271429 | C2 | semidirect |
| 7. #14271339 | C2 | semidirect |
| 8. #14271338 | C2 | semidirect |
| 9. #14271279 | C2 | semidirect |
| 10. #14271278 | C2 | semidirect |
| 11. C29×#473 | C2 | semidirect |
| 13. #11745362 | C22 | semidirect |
| 15. C2×Q16×C29 | C22 | semidirect |
| 18. #11745309 | C22 | semidirect |
| 19. #11745304 | C22 | semidirect |
| 20. C2×#90784 | C22 | semidirect |
| 30. #11745270 | C22 | semidirect |
| 31. #11745269 | C22 | semidirect |
| 36. #11745263 | C22 | semidirect |
| 37. C29×#108 | C22 | semidirect |
| 38. C29×#101 | C22 | semidirect |
| 40. #11745173 | C22 | semidirect |
| 41. #11745173 | C22 | semidirect |
| 42. #11745171 | C22 | semidirect |
| 43. #11745170 | C22 | semidirect |
| 44. C8×Dic29 | C22 | semidirect |
| 148. #473 | D29 | semidirect |
| 177. C2×Q16 | C2×D29 | semidirect |
| 187. #108 | C2×D29 | semidirect |
| 191. #101 | C2×D29 | semidirect |
| 194. C29 | #3290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271976 | 2 |
| #14271972 | 2 |
| #14271968 | 2 |
| #14271548 | 2 |
| #14271434 | 2 |
| #14271429 | 2 |
| #14271339 | 2 |
| #14271338 | 2 |
| #14271279 | 2 |
| #14271278 | 2 |
| C29×#473 | 2 |
| #3290 | 29 |