Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1310 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1310 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. #26029510 | C2 | semidirect |
| 3. #26019209 | C2 | semidirect |
| 4. #26019175 | C2 | semidirect |
| 5. #26018785 | C2 | semidirect |
| 6. #26018579 | C2 | semidirect |
| 7. C2×#543×C89 | C2 | semidirect |
| 12. #19151753 | C22 | semidirect |
| 13. #19151748 | C22 | semidirect |
| 21. #19151335 | C22 | semidirect |
| 57. C22×Q8×C89 | D4 | semidirect |
| 70. C22⋊Q8×C89 | D4 | semidirect |
| 75. C2×C4⋊C4×C89 | D4 | semidirect |
| 166. C23×C89 | #137 | semidirect |
| 246. C2×#543 | D89 | semidirect |
| 253. C89 | #18133 | semidirect |
| 284. C22×Q8 | C22⋊D89 | semidirect |
| 305. C22⋊Q8 | C22⋊D89 | semidirect |
| 311. C2×C4⋊C4 | C22⋊D89 | semidirect |
| 417. C23 | #15668043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029510 | 2 |
| #26023571 | 2 |
| #26019209 | 2 |
| #26019175 | 2 |
| #26018785 | 2 |
| #26018579 | 2 |
| C2×#543×C89 | 2 |
| #18133 | 89 |