Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 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×#20294097 | C2 | semidirect |
| 2. C2×#20294085 | C2 | semidirect |
| 3. C2×#20294082 | C2 | semidirect |
| 4. #28357143 | C2 | semidirect |
| 5. #28357140 | C2 | semidirect |
| 6. C22⋊#16812358 | C2 | semidirect |
| 7. #121×C433 | C2 | semidirect |
| 25. Dic866 | D4 | semidirect |
| 27. D1732 | D4 | semidirect |
| 64. C433 | #449 | semidirect |
| 69. #121 | D433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294097 | 2 |
| C2×#20294085 | 2 |
| C2×#20294082 | 2 |
| #28357143 | 2 |
| #28357140 | 2 |
| C22⋊#16812358 | 2 |
| #121×C433 | 2 |
| #449 | 433 |