Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
158 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 2. #26014948 | C2 | semidirect |
| 3. #26014907 | C2 | semidirect |
| 4. #26014906 | C2 | semidirect |
| 5. #99×C353 | C2 | semidirect |
| 8. C2×Dic706 | C4 | semidirect |
| 9. C2×C22⋊D353 | C4 | semidirect |
| 11. C22×Dic353 | C4 | semidirect |
| 13. C2×C4×D353 | C4 | semidirect |
| 57. C353 | #410 | semidirect |
| 63. #99 | D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150736 | 2 |
| #26014948 | 2 |
| #26014907 | 2 |
| #26014906 | 2 |
| #99×C353 | 2 |
| #410 | 353 |