Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
104 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 40 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. #26015080 | C2 | semidirect |
| 2. #26015079 | C2 | semidirect |
| 3. #26015063 | C2 | semidirect |
| 4. #26015057 | C2 | semidirect |
| 5. #26015056 | C2 | semidirect |
| 6. #26015046 | C2 | semidirect |
| 18. #19150727 | C4 | semidirect |
| 19. #19150726 | C4 | semidirect |
| 20. #19150722 | C4 | semidirect |
| 22. SD16×C353 | C4 | semidirect |
| 51. C353 | #444 | semidirect |
| 64. SD16 | #13083443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26015080 | 2 |
| #26015079 | 2 |
| #26015063 | 2 |
| #26015057 | 2 |
| #26015056 | 2 |
| #26015046 | 2 |
| #26015013 | 2 |
| #444 | 353 |