Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26014987 | C2 | semidirect |
| 2. #26014983 | C2 | semidirect |
| 3. #26014981 | C2 | semidirect |
| 4. #26014976 | C2 | semidirect |
| 6. Q8×Dic353 | C2 | semidirect |
| 7. #26014954 | C2 | semidirect |
| 8. #26014952 | C2 | semidirect |
| 9. #26014950 | C2 | semidirect |
| 10. C2×C4×Dic353 | C2 | semidirect |
| 11. C22⋊Q8×C353 | C2 | semidirect |
| 74. C353 | #529 | semidirect |
| 80. C22⋊Q8 | D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26014987 | 2 |
| #26014983 | 2 |
| #26014981 | 2 |
| #26014976 | 2 |
| #26014966 | 2 |
| Q8×Dic353 | 2 |
| #26014954 | 2 |
| #26014952 | 2 |
| #26014950 | 2 |
| C2×C4×Dic353 | 2 |
| C22⋊Q8×C353 | 2 |
| #529 | 353 |