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. C2×#11745263 | C2 | semidirect |
| 2. #14271737 | C2 | semidirect |
| 4. #14271406 | C2 | semidirect |
| 5. #14271389 | C2 | semidirect |
| 6. #14271201 | C2 | semidirect |
| 7. #14271172 | C2 | semidirect |
| 8. #14271168 | C2 | semidirect |
| 9. C22×SD16×C29 | C2 | semidirect |
| 19. #11745308 | C22 | semidirect |
| 29. C2×#90772 | C22 | semidirect |
| 30. C2×C8×D29 | C22 | semidirect |
| 31. #11745183 | C22 | semidirect |
| 33. #11745166 | C22 | semidirect |
| 34. #11745165 | C22 | semidirect |
| 55. C2×C8×C29 | D4 | semidirect |
| 116. C22×SD16 | D29 | semidirect |
| 155. C29 | #3057 | semidirect |
| 180. C2×C8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745263 | 2 |
| #14271737 | 2 |
| #14271730 | 2 |
| #14271406 | 2 |
| #14271389 | 2 |
| #14271201 | 2 |
| #14271172 | 2 |
| #14271168 | 2 |
| C22×SD16×C29 | 2 |
| #3057 | 29 |