Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
322 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 127 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. C22×Dic866 | C2 | semidirect |
| 3. #28357198 | C2 | direct (N × H) |
| 4. C2×#20294076 | C2 | semidirect |
| 5. C2×#20294076 | C2 | semidirect |
| 8. C2×C4⋊C4×C433 | C2 | semidirect |
| 11. C2×Dic866 | C22 | semidirect |
| 17. #20294076 | C22 | semidirect |
| 18. #20294076 | C22 | semidirect |
| 24. C4⋊C4×C433 | C22 | semidirect |
| 27. C22×D433 | Q8 | semidirect |
| 51. C2×D433 | C2×Q8 | semidirect |
| 58. C2×C433 | C22⋊Q8 | semidirect |
| 63. C433 | C2×C22⋊Q8 | semidirect |
| 70. C2×C4⋊C4 | D433 | semidirect |
| 86. C4⋊C4 | C2×D433 | semidirect |
| 123. C2 | #28357198 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic866 | 2 |
| C22×C4×D433 | 2 |
| #28357198 | 2 |
| C2×#20294076 | 2 |
| C2×#20294074 | 2 |
| C2×C4⋊C4×C433 | 2 |
| C2×C22⋊Q8 | 433 |