Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
388 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 77 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. C22⋊C8×D29 | C2 | semidirect |
| 3. #95×D29 | C2 | semidirect |
| 4. #14270898 | C2 | semidirect |
| 5. #14270897 | C2 | semidirect |
| 6. #14270896 | C2 | semidirect |
| 7. C29×#327 | C2 | semidirect |
| 9. C2×D4×D29 | C4 | semidirect |
| 14. #11745300 | C4 | semidirect |
| 17. #11745257 | C4 | semidirect |
| 18. C4⋊C4×D29 | C4 | semidirect |
| 21. C29×C22⋊C8 | C22 | semidirect |
| 22. C29×#95 | C22 | semidirect |
| 24. #11745179 | C22 | semidirect |
| 25. C22⋊#6597 | C22 | semidirect |
| 30. C2×D4×C29 | C2×C4 | semidirect |
| 42. C2×D116 | C2×C4 | semidirect |
| 53. C4⋊C4×C29 | C2×C4 | semidirect |
| 58. C4⋊Dic29 | C2×C4 | semidirect |
| 140. #327 | D29 | direct (N × H) |
| 149. D29 | #327 | direct (N × H) |
| 165. C22⋊C8 | C2×D29 | semidirect |
| 168. #95 | C2×D29 | semidirect |
| 169. C29 | C2×#327 | semidirect |
| 181. C2×D4 | C4×D29 | semidirect |
| 200. C4⋊C4 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #121×D29 | 2 |
| C22⋊C8×D29 | 2 |
| #95×D29 | 2 |
| #14270898 | 2 |
| #14270897 | 2 |
| #14270896 | 2 |
| C29×#327 | 2 |
| C2×#327 | 29 |