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×#20294084 | C2 | semidirect |
| 3. C4×D1732 | C2 | semidirect |
| 4. C4⋊#16812358 | C2 | semidirect |
| 5. #28357144 | C2 | semidirect |
| 6. #28357141 | C2 | semidirect |
| 7. #124×C433 | C2 | semidirect |
| 55. C433 | #463 | semidirect |
| 59. #124 | D433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294084 | 2 |
| C2×#20294082 | 2 |
| C4×D1732 | 2 |
| C4⋊#16812358 | 2 |
| #28357144 | 2 |
| #28357141 | 2 |
| #124×C433 | 2 |
| #463 | 433 |