Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
114 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 4. C4⋊#16812358 | C2 | semidirect |
| 5. #28357149 | C2 | semidirect |
| 6. #28357149 | C2 | semidirect |
| 7. C4⋊C8×C433 | C2 | semidirect |
| 49. C433 | #424 | semidirect |
| 57. C4⋊C8 | D433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294080 | 2 |
| C2×C8×D433 | 2 |
| #28357177 | 2 |
| C4⋊#16812358 | 2 |
| #28357149 | 2 |
| C4⋊C8×C433 | 2 |
| #424 | 433 |