Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
2502 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2502 conjugacy classes of subgroups — too many to draw. Only its 667 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. C22×#15668006 | C2 | semidirect |
| 2. #26028326 | C2 | direct (N × H) |
| 3. C2×#19151528 | C2 | semidirect |
| 4. C2×#19151520 | C2 | semidirect |
| 6. C2×#384×C89 | C2 | semidirect |
| 9. C2×#15668006 | C22 | semidirect |
| 14. #19151528 | C22 | semidirect |
| 15. #19151520 | C22 | semidirect |
| 22. #384×C89 | C22 | semidirect |
| 45. C2×C42×C89 | D4 | semidirect |
| 73. C42×C89 | C2×D4 | semidirect |
| 113. C2×C89 | #2823 | semidirect |
| 123. C2×#384 | D89 | semidirect |
| 124. C89 | C2×#2823 | semidirect |
| 138. #384 | C2×D89 | semidirect |
| 161. C2×C42 | D356 | semidirect |
| 191. C42 | C2×D356 | semidirect |
| 231. C2 | #26028326 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668006 | 2 |
| #26028326 | 2 |
| C2×#19151528 | 2 |
| C2×#19151520 | 2 |
| C2×#19151515 | 2 |
| C2×#384×C89 | 2 |
| C2×#2823 | 89 |