Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
112 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 43 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×#20294087 | C2 | semidirect |
| 4. C4⋊#16812358 | C2 | semidirect |
| 5. #28357143 | C2 | semidirect |
| 7. C4×Q8×C433 | C2 | semidirect |
| 51. C433 | #464 | semidirect |
| 56. C4×Q8 | D433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294087 | 2 |
| C2×#20294084 | 2 |
| #28357208 | 2 |
| C4⋊#16812358 | 2 |
| #28357143 | 2 |
| #28357140 | 2 |
| C4×Q8×C433 | 2 |
| #464 | 433 |