Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #14271791 | C2 | semidirect |
| 2. #14271527 | C2 | semidirect |
| 3. #14271522 | C2 | semidirect |
| 4. #14271517 | C2 | semidirect |
| 5. #14271509 | C2 | semidirect |
| 6. #14271168 | C2 | semidirect |
| 7. #14271164 | C2 | semidirect |
| 8. #14271159 | C2 | semidirect |
| 9. C2×#11745180 | C2 | semidirect |
| 10. #14271119 | C2 | semidirect |
| 27. #11745232 | C22 | semidirect |
| 28. #11745231 | C22 | semidirect |
| 29. #11745183 | C22 | semidirect |
| 30. #11745183 | C22 | semidirect |
| 31. #11745183 | C22 | semidirect |
| 36. #11745180 | C22 | semidirect |
| 37. #11745180 | C22 | semidirect |
| 38. #11745180 | C22 | semidirect |
| 39. #11745151 | C22 | semidirect |
| 40. C4×#6597 | C22 | semidirect |
| 176. C29 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271791 | 2 |
| #14271527 | 2 |
| #14271522 | 2 |
| #14271517 | 2 |
| #14271509 | 2 |
| #14271168 | 2 |
| #14271164 | 2 |
| #14271159 | 2 |
| C2×#11745180 | 2 |
| #14271119 | 2 |
| C29×#535 | 2 |
| #3136 | 29 |