Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
432 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 88 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. C22×D29⋊C8 | C2 | semidirect |
| 2. C2×#11745223 | C2 | semidirect |
| 3. #14272105 | C2 | semidirect |
| 4. #14272036 | C2 | semidirect |
| 15. C29×#121 | C4 | semidirect |
| 17. #11745300 | C4 | semidirect |
| 18. #11745292 | C4 | semidirect |
| 19. #11745257 | C4 | semidirect |
| 55. D29⋊C8 | D4 | semidirect |
| 111. C22×C29 | #102 | semidirect |
| 122. C2×D29 | #102 | semidirect |
| 161. #121 | #1181 | semidirect |
| 168. C29 | #1893 | semidirect |
| 268. C22 | #11745223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D29⋊C8 | 2 |
| C2×#11745223 | 2 |
| #14272105 | 2 |
| #14272036 | 2 |
| #121×D29 | 2 |
| #1893 | 29 |