Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
140 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 140 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×#20294082 | C2 | semidirect |
| 2. #28357216 | C2 | semidirect |
| 3. D4×Dic433 | C2 | semidirect |
| 4. #28357149 | C2 | semidirect |
| 5. #28357142 | C2 | semidirect |
| 6. #28357141 | C2 | semidirect |
| 7. C2×D8×C433 | C2 | semidirect |
| 36. D4×C433 | D4 | semidirect |
| 53. Dic433 | D8 | semidirect |
| 60. C433 | #459 | semidirect |
| 63. C2×D8 | D433 | semidirect |
| 92. D4 | C22⋊D433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294082 | 2 |
| #28357216 | 2 |
| D4×Dic433 | 2 |
| #28357149 | 2 |
| #28357142 | 2 |
| #28357141 | 2 |
| C2×D8×C433 | 2 |
| #459 | 433 |