Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1224 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 249 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. C24×Dic29 | C2 | semidirect |
| 3. C2×#11745243 | C2 | semidirect |
| 4. #14271040 | C2 | semidirect |
| 5. #14271035 | C2 | semidirect |
| 6. C22⋊C4×Dic29 | C2 | semidirect |
| 7. C29×#379 | C2 | semidirect |
| 13. C22×C4×D29 | C22 | semidirect |
| 16. #11745315 | C4 | semidirect |
| 18. C2×#90781 | C22 | semidirect |
| 19. C2×#90779 | C22 | semidirect |
| 20. C2×C4×Dic29 | C22 | semidirect |
| 22. #11745179 | C22 | semidirect |
| 25. C24×C29 | C2×C4 | semidirect |
| 32. C2×C22⋊D29 | C2×C4 | semidirect |
| 37. C22×Dic29 | D4 | semidirect |
| 44. C22⋊Dic29 | C2×C4 | semidirect |
| 59. C22×D29 | C22×C4 | semidirect |
| 69. C2×Dic29 | C22×C4 | semidirect |
| 79. C22×C29 | C4×D4 | semidirect |
| 90. Dic29 | #120 | semidirect |
| 96. #379 | D29 | semidirect |
| 118. C29 | C4×#120 | semidirect |
| 122. C24 | C4×D29 | semidirect |
| 177. C22 | #11745243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic29 | 2 |
| C2×#11745315 | 2 |
| C2×#11745243 | 2 |
| #14271040 | 2 |
| #14271035 | 2 |
| C22⋊C4×Dic29 | 2 |
| C29×#379 | 2 |
| C4×#120 | 29 |