Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. #14271713 | C2 | semidirect |
| 2. C2×C4×D116 | C2 | semidirect |
| 3. #14271477 | C2 | semidirect |
| 4. #14271444 | C2 | semidirect |
| 5. #14271359 | C2 | semidirect |
| 6. #14271299 | C2 | semidirect |
| 7. C4×D232 | C2 | semidirect |
| 8. C29×#431 | C2 | semidirect |
| 19. #11745236 | C22 | semidirect |
| 25. C4×D116 | C22 | semidirect |
| 26. #11745231 | C22 | semidirect |
| 27. C29×C4⋊C8 | C22 | semidirect |
| 29. C4×C8×C29 | C22 | semidirect |
| 31. #11745169 | C22 | semidirect |
| 32. #11745166 | C22 | semidirect |
| 73. C2×C4×C29 | D8 | semidirect |
| 89. D116 | #41 | semidirect |
| 122. #431 | D29 | semidirect |
| 148. C4⋊C8 | C2×D29 | semidirect |
| 152. C4×C8 | C2×D29 | semidirect |
| 153. C29 | #3100 | semidirect |
| 208. C2×C4 | D232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271713 | 2 |
| C2×C4×D116 | 2 |
| #14271477 | 2 |
| #14271444 | 2 |
| #14271359 | 2 |
| #14271299 | 2 |
| C4×D232 | 2 |
| C29×#431 | 2 |
| #3100 | 29 |