Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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×Q8×D353 | C2 | semidirect |
| 3. #26014991 | C2 | semidirect |
| 4. #26014978 | C2 | semidirect |
| 5. #26014977 | C2 | semidirect |
| 6. #26014974 | C2 | semidirect |
| 7. #26014972 | C2 | semidirect |
| 8. #26014971 | C2 | semidirect |
| 9. #26014968 | C2 | semidirect |
| 10. #26014950 | C2 | semidirect |
| 11. C22⋊Q8×C353 | C2 | semidirect |
| 83. C353 | #536 | semidirect |
| 94. C22⋊Q8 | D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150737 | 2 |
| C2×Q8×D353 | 2 |
| #26014991 | 2 |
| #26014978 | 2 |
| #26014977 | 2 |
| #26014974 | 2 |
| #26014972 | 2 |
| #26014971 | 2 |
| #26014968 | 2 |
| #26014950 | 2 |
| C22⋊Q8×C353 | 2 |
| #536 | 353 |