Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
792 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 218 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. C23×#6599 | C2 | semidirect |
| 3. #14272136 | C2 | direct (N × H) |
| 4. C2×#11745219 | C2 | semidirect |
| 5. C2×C22⋊#6599 | C2 | semidirect |
| 19. C2×#90800 | C22 | semidirect |
| 23. C22×#6599 | C22 | semidirect |
| 24. C22⋊#6599 | C22 | semidirect |
| 25. #11745219 | C22 | semidirect |
| 124. C2×C29 | #408 | semidirect |
| 147. C29 | C2×#408 | semidirect |
| 240. C2 | #14272136 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90800 | 2 |
| C23×#6599 | 2 |
| #14272136 | 2 |
| C2×#11745219 | 2 |
| C2×C22⋊#6599 | 2 |
| C22×#90807 | 2 |
| C2×#408 | 29 |