Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
218 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26014987 | C2 | semidirect |
| 2. #26014985 | C2 | semidirect |
| 3. #26014982 | C2 | semidirect |
| 4. #26014982 | C2 | semidirect |
| 5. #26014977 | C2 | semidirect |
| 6. #26014975 | C2 | semidirect |
| 7. #26014974 | C2 | semidirect |
| 8. #26014974 | C2 | semidirect |
| 9. #26014968 | C2 | semidirect |
| 10. #26014968 | C2 | semidirect |
| 12. #26014954 | C2 | semidirect |
| 13. C4×C22⋊D353 | C2 | semidirect |
| 14. C4⋊C4×D353 | C2 | semidirect |
| 15. C22⋊Q8×C353 | C2 | semidirect |
| 103. C353 | #539 | semidirect |
| 115. C22⋊Q8 | D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26014987 | 2 |
| #26014985 | 2 |
| #26014982 | 2 |
| #26014977 | 2 |
| #26014975 | 2 |
| #26014974 | 2 |
| #26014968 | 2 |
| #26014965 | 2 |
| #26014954 | 2 |
| C4×C22⋊D353 | 2 |
| C4⋊C4×D353 | 2 |
| C22⋊Q8×C353 | 2 |
| #539 | 353 |