Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
188 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 47 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. C2×#19150726 | C2 | semidirect |
| 3. #26014971 | C2 | semidirect |
| 4. #26014914 | C2 | semidirect |
| 5. C22⋊C8×C353 | C2 | semidirect |
| 7. C2×Dic706 | C22 | semidirect |
| 12. C4⋊Dic353 | C22 | semidirect |
| 16. C2×C8×C353 | C22 | semidirect |
| 34. C22×C353 | SD16 | semidirect |
| 49. C353 | #450 | semidirect |
| 55. C22⋊C8 | D353 | semidirect |
| 63. C2×C8 | C2×D353 | semidirect |
| 88. C22 | #19150726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1412 | 2 |
| C2×#19150726 | 2 |
| #26014971 | 2 |
| #26014914 | 2 |
| C22⋊C8×C353 | 2 |
| #450 | 353 |