Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1172 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1172 conjugacy classes of subgroups — too many to draw. Only its 183 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. #26031054 | C2 | semidirect |
| 3. #26019277 | C2 | semidirect |
| 4. #26019175 | C2 | semidirect |
| 5. #26018772 | C2 | semidirect |
| 6. #26018579 | C2 | semidirect |
| 7. C2×#543×C89 | C2 | semidirect |
| 11. #19151931 | C22 | semidirect |
| 14. #19151748 | C22 | semidirect |
| 21. #19151335 | C22 | semidirect |
| 56. C22×Q8×C89 | D4 | semidirect |
| 69. C22⋊Q8×C89 | D4 | semidirect |
| 74. C2×C4⋊C4×C89 | D4 | semidirect |
| 235. C2×#543 | D89 | semidirect |
| 242. C89 | #18318 | semidirect |
| 269. C22×Q8 | C22⋊D89 | semidirect |
| 288. C22⋊Q8 | C22⋊D89 | semidirect |
| 298. C2×C4⋊C4 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031054 | 2 |
| #26025183 | 2 |
| #26019277 | 2 |
| #26019175 | 2 |
| #26018772 | 2 |
| #26018579 | 2 |
| C2×#543×C89 | 2 |
| #18318 | 89 |