Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 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. #14271730 | C2 | semidirect |
| 3. #14271413 | C2 | semidirect |
| 4. #14271396 | C2 | semidirect |
| 5. #14271201 | C2 | semidirect |
| 6. #14271168 | C2 | semidirect |
| 7. C22×D8×C29 | C2 | semidirect |
| 16. #11745300 | C22 | semidirect |
| 21. C2×#90772 | C22 | semidirect |
| 22. C2×C8×D29 | C22 | semidirect |
| 23. #11745180 | C22 | semidirect |
| 24. #11745166 | C22 | semidirect |
| 25. #11745165 | C22 | semidirect |
| 41. C2×C8×C29 | D4 | semidirect |
| 89. C22×D8 | D29 | semidirect |
| 119. C29 | #3058 | semidirect |
| 139. 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 |
| #14271730 | 2 |
| #14271413 | 2 |
| #14271396 | 2 |
| #14271201 | 2 |
| #14271168 | 2 |
| C22×D8×C29 | 2 |
| #3058 | 29 |