Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
764 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 202 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×#90800 | C2 | semidirect |
| 2. #14272136 | C2 | semidirect |
| 3. #14272135 | C2 | semidirect |
| 4. #14272133 | C2 | semidirect |
| 18. C2×#90800 | C22 | semidirect |
| 19. C22×#6599 | C22 | semidirect |
| 20. C22⋊#6599 | C22 | semidirect |
| 21. #11745219 | C22 | semidirect |
| 129. C29 | #2879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90800 | 2 |
| #14272136 | 2 |
| #14272135 | 2 |
| #14272133 | 2 |
| C22×#90807 | 2 |
| #2879 | 29 |