Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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×#20294086 | C2 | semidirect |
| 3. #28357208 | C2 | semidirect |
| 4. C4×D1732 | C2 | semidirect |
| 5. #28357145 | C2 | semidirect |
| 6. #28357142 | C2 | semidirect |
| 7. C4⋊C8×C433 | C2 | semidirect |
| 55. C433 | #463 | semidirect |
| 61. C4⋊C8 | D433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294086 | 2 |
| C2×D3464 | 2 |
| #28357208 | 2 |
| C4×D1732 | 2 |
| #28357145 | 2 |
| #28357142 | 2 |
| C4⋊C8×C433 | 2 |
| #463 | 433 |