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×#20294096 | C2 | semidirect |
| 2. C2×#20294086 | C2 | semidirect |
| 3. C2×#20294082 | C2 | semidirect |
| 4. #28357195 | C2 | semidirect |
| 5. #28357143 | C2 | semidirect |
| 6. #28357132 | C2 | semidirect |
| 7. #102×C433 | C2 | semidirect |
| 26. Dic866 | D4 | semidirect |
| 39. D4×C433 | D4 | semidirect |
| 64. C433 | #449 | semidirect |
| 71. #102 | D433 | semidirect |
| 98. D4 | D1732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294096 | 2 |
| C2×#20294086 | 2 |
| C2×#20294082 | 2 |
| #28357195 | 2 |
| #28357143 | 2 |
| #28357132 | 2 |
| #102×C433 | 2 |
| #449 | 433 |