Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
450 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 450 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. #14271694 | C2 | semidirect |
| 2. C2×#11745255 | C2 | semidirect |
| 3. #14271493 | C2 | semidirect |
| 4. #14271466 | C2 | semidirect |
| 5. #14271377 | C2 | semidirect |
| 6. #14271316 | C2 | semidirect |
| 8. #14271272 | C2 | semidirect |
| 9. #14271262 | C2 | semidirect |
| 10. #14271217 | C2 | semidirect |
| 11. C29×#480 | C2 | semidirect |
| 16. #11745298 | C22 | semidirect |
| 19. D4×Dic29 | C22 | semidirect |
| 29. #11745252 | C22 | semidirect |
| 30. #11745249 | C22 | semidirect |
| 33. C29×#107 | C22 | semidirect |
| 34. C29×#102 | C22 | semidirect |
| 38. #11745163 | C22 | semidirect |
| 39. #11745162 | C22 | semidirect |
| 40. #11745158 | C22 | semidirect |
| 42. #11745156 | C22 | semidirect |
| 138. #480 | D29 | semidirect |
| 173. #107 | C2×D29 | semidirect |
| 179. #102 | C2×D29 | semidirect |
| 183. C29 | #3114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271694 | 2 |
| C2×#11745255 | 2 |
| #14271493 | 2 |
| #14271466 | 2 |
| #14271377 | 2 |
| #14271316 | 2 |
| #14271296 | 2 |
| #14271272 | 2 |
| #14271262 | 2 |
| #14271217 | 2 |
| C29×#480 | 2 |
| #3114 | 29 |