Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
222 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26014991 | C2 | semidirect |
| 2. #26014990 | C2 | semidirect |
| 3. #26014982 | C2 | semidirect |
| 6. Q8×Dic353 | C2 | semidirect |
| 7. #26014957 | C2 | semidirect |
| 8. #26014957 | C2 | semidirect |
| 38. C2×Dic353 | Q8 | semidirect |
| 70. C353 | #533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26014991 | 2 |
| #26014990 | 2 |
| #26014982 | 2 |
| #26014971 | 2 |
| #26014969 | 2 |
| Q8×Dic353 | 2 |
| #26014957 | 2 |
| #26014948 | 2 |
| C2×C4×Dic353 | 2 |
| C22⋊Q8×C353 | 2 |
| #533 | 353 |