Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26015038 | C2 | semidirect |
| 2. #26015023 | C2 | semidirect |
| 3. #26015017 | C2 | semidirect |
| 4. #26015012 | C2 | semidirect |
| 5. C2×#19150724 | C2 | semidirect |
| 6. #26014999 | C2 | semidirect |
| 7. 2−1+4×C353 | C2 | semidirect |
| 12. #19150727 | C22 | semidirect |
| 13. #19150725 | C22 | semidirect |
| 14. #19150724 | C22 | semidirect |
| 15. #19150724 | C22 | semidirect |
| 16. #19150722 | C22 | semidirect |
| 17. #19150721 | C22 | semidirect |
| 18. C2×#15667725 | C22 | semidirect |
| 21. #41×C353 | C22 | semidirect |
| 23. C2×Q8×C353 | C22 | semidirect |
| 53. C353 | #577 | semidirect |
| 55. 2−1+4 | D353 | semidirect |
| 66. #41 | C2×D353 | semidirect |
| 68. C2×Q8 | C2×D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26015038 | 2 |
| #26015023 | 2 |
| #26015017 | 2 |
| #26015012 | 2 |
| C2×#19150724 | 2 |
| #26014999 | 2 |
| 2−1+4×C353 | 2 |
| #577 | 353 |