Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×#11745254 | C2 | semidirect |
| 3. #14271506 | C2 | semidirect |
| 4. #14271499 | C2 | semidirect |
| 5. #14271493 | C2 | semidirect |
| 6. #14271485 | C2 | semidirect |
| 7. #14271479 | C2 | semidirect |
| 8. #14271200 | C2 | semidirect |
| 9. #14271156 | C2 | semidirect |
| 10. C22⋊C8×D29 | C2 | semidirect |
| 11. C29×#480 | C2 | semidirect |
| 32. C29×#107 | C22 | semidirect |
| 33. C29×#102 | C22 | semidirect |
| 35. #11745180 | C22 | semidirect |
| 38. #11745166 | C22 | semidirect |
| 39. #11745164 | C22 | semidirect |
| 40. #11745158 | C22 | semidirect |
| 41. #11745156 | C22 | semidirect |
| 42. #11745156 | C22 | semidirect |
| 144. #480 | D29 | semidirect |
| 176. #107 | C2×D29 | semidirect |
| 182. #102 | C2×D29 | semidirect |
| 186. C29 | #3091 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271673 | 2 |
| C2×#11745254 | 2 |
| #14271506 | 2 |
| #14271499 | 2 |
| #14271493 | 2 |
| #14271485 | 2 |
| #14271479 | 2 |
| #14271200 | 2 |
| #14271156 | 2 |
| C22⋊C8×D29 | 2 |
| C29×#480 | 2 |
| #3091 | 29 |