Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14271962 | C2 | semidirect |
| 2. C2×#11745281 | C2 | semidirect |
| 3. #131×D29 | C2 | semidirect |
| 4. #14271435 | C2 | semidirect |
| 5. #14271434 | C2 | semidirect |
| 6. #14271433 | C2 | semidirect |
| 7. #14271429 | C2 | semidirect |
| 8. #14271428 | C2 | semidirect |
| 9. #108×D29 | C2 | semidirect |
| 10. #14271146 | C2 | semidirect |
| 11. C29×#473 | C2 | semidirect |
| 15. C2×Q16×C29 | C22 | semidirect |
| 20. C2×#90784 | C22 | semidirect |
| 35. C2×D232 | C22 | semidirect |
| 40. C29×#108 | C22 | semidirect |
| 41. C29×#101 | C22 | semidirect |
| 42. #11745184 | C22 | semidirect |
| 43. #11745171 | C22 | semidirect |
| 44. #11745171 | C22 | semidirect |
| 45. #11745170 | C22 | semidirect |
| 46. #11745167 | C22 | semidirect |
| 164. #473 | D29 | semidirect |
| 192. C2×Q16 | C2×D29 | semidirect |
| 208. #108 | C2×D29 | semidirect |
| 210. #101 | C2×D29 | semidirect |
| 213. C29 | #3067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271962 | 2 |
| C2×#11745281 | 2 |
| #131×D29 | 2 |
| #14271435 | 2 |
| #14271434 | 2 |
| #14271433 | 2 |
| #14271429 | 2 |
| #14271428 | 2 |
| #108×D29 | 2 |
| #14271146 | 2 |
| C29×#473 | 2 |
| #3067 | 29 |