Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
246 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 111 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. #28357213 | C2 | direct (N × H) |
| 2. C2×C4⋊Dic433 | C2 | semidirect |
| 3. C2×#20294076 | C2 | semidirect |
| 4. C2×#20294076 | C2 | semidirect |
| 7. C2×C4×Dic433 | C2 | semidirect |
| 13. C4⋊Dic433 | C22 | semidirect |
| 14. #20294076 | C22 | semidirect |
| 15. #20294076 | C22 | semidirect |
| 18. C4×Dic433 | C22 | semidirect |
| 55. C2×C433 | #126 | semidirect |
| 59. C433 | C2×#126 | semidirect |
| 115. C2 | #28357213 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28357213 | 2 |
| C2×C4⋊Dic433 | 2 |
| C2×#20294076 | 2 |
| C2×C22⋊Dic433 | 2 |
| C2×C4×Dic433 | 2 |
| C2×C22⋊C4×C433 | 2 |
| C2×#126 | 433 |