Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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×#11745269 | C2 | semidirect |
| 2. C22×#90772 | C2 | semidirect |
| 4. #14271240 | C2 | semidirect |
| 5. #14271233 | C2 | semidirect |
| 6. #14271129 | C2 | semidirect |
| 7. #14271126 | C2 | semidirect |
| 8. #14271119 | C2 | semidirect |
| 9. C29×#424 | C2 | semidirect |
| 21. C2×#90772 | C22 | semidirect |
| 22. C2×C8×D29 | C22 | semidirect |
| 28. C29×C4⋊C8 | C22 | semidirect |
| 30. #11745168 | C22 | semidirect |
| 31. #11745151 | C22 | semidirect |
| 32. C4×#6597 | C22 | semidirect |
| 58. C2×#6597 | D4 | semidirect |
| 114. #424 | D29 | semidirect |
| 141. C4⋊C8 | C2×D29 | semidirect |
| 146. C29 | #2930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745269 | 2 |
| C22×#90772 | 2 |
| #14271675 | 2 |
| #14271240 | 2 |
| #14271233 | 2 |
| #14271129 | 2 |
| #14271126 | 2 |
| #14271119 | 2 |
| C29×#424 | 2 |
| #2930 | 29 |