Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
392 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 156 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. #14272187 | C2 | semidirect |
| 2. #14272183 | C2 | semidirect |
| 3. #14272180 | C2 | semidirect |
| 4. #14272168 | C2 | semidirect |
| 5. D29⋊(C4⋊C8) | C2 | semidirect |
| 7. #14272128 | C2 | semidirect |
| 139. C29 | #2925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272187 | 2 |
| #14272183 | 2 |
| #14272180 | 2 |
| #14272168 | 2 |
| D29⋊(C4⋊C8) | 2 |
| #14272137 | 2 |
| #14272128 | 2 |
| C4×#90807 | 2 |
| #2925 | 29 |