Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
524 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 170 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. #14272112 | C2 | semidirect |
| 3. C4×C4⋊#1181 | C2 | semidirect |
| 5. #14272099 | C2 | semidirect |
| 6. C42×#1181 | C2 | semidirect |
| 14. C29×#117 | C4 | semidirect |
| 15. #11745288 | C4 | semidirect |
| 16. #11745254 | C4 | semidirect |
| 19. #11745239 | C4 | semidirect |
| 20. #11745234 | C4 | semidirect |
| 21. #11745234 | C4 | semidirect |
| 122. #117 | #1181 | semidirect |
| 135. C29 | #2298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272113 | 2 |
| #14272112 | 2 |
| C4×C4⋊#1181 | 2 |
| C4×C22⋊#1181 | 2 |
| #14272099 | 2 |
| C42×#1181 | 2 |
| #117×D29 | 2 |
| #2298 | 29 |