Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
112 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 41 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 |
|---|---|---|
| 3. Q8×Dic353 | C2 | semidirect |
| 4. #26014921 | C2 | semidirect |
| 5. #26014916 | C2 | semidirect |
| 7. C2×Q16×C353 | C2 | semidirect |
| 51. C353 | #464 | semidirect |
| 53. C2×Q16 | D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150724 | 2 |
| #26014981 | 2 |
| Q8×Dic353 | 2 |
| #26014921 | 2 |
| #26014916 | 2 |
| #26014914 | 2 |
| C2×Q16×C353 | 2 |
| #464 | 353 |