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. #26015039 | C2 | semidirect |
| 2. #26015038 | C2 | semidirect |
| 3. #26015025 | C2 | semidirect |
| 4. #26015020 | C2 | semidirect |
| 5. #26015014 | C2 | semidirect |
| 6. C2×#19150726 | C2 | semidirect |
| 7. #131×C353 | C2 | semidirect |
| 10. #19150737 | C22 | semidirect |
| 12. C2×Dic706 | C22 | semidirect |
| 16. Dic1412 | C22 | semidirect |
| 17. #19150726 | C22 | semidirect |
| 18. #19150726 | C22 | semidirect |
| 19. #19150726 | C22 | semidirect |
| 20. D2824 | C22 | semidirect |
| 22. M16×C353 | C22 | semidirect |
| 23. C2×C8×C353 | C22 | semidirect |
| 53. C353 | #577 | semidirect |
| 61. #131 | D353 | semidirect |
| 76. M16 | C2×D353 | semidirect |
| 77. C2×C8 | C2×D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26015039 | 2 |
| #26015038 | 2 |
| #26015025 | 2 |
| #26015020 | 2 |
| #26015014 | 2 |
| C2×#19150726 | 2 |
| #131×C353 | 2 |
| #577 | 353 |