Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
894 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 894 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26020197 | C2 | semidirect |
| 4. #26018785 | C2 | semidirect |
| 5. #26018579 | C2 | semidirect |
| 6. #26018105 | C2 | semidirect |
| 7. C89×#2561 | C2 | semidirect |
| 58. C22⋊#10623494 | D4 | semidirect |
| 63. C22×Q8×C89 | D4 | semidirect |
| 71. C2×C4⋊C4×C89 | D4 | semidirect |
| 82. C2×C42×C89 | D4 | semidirect |
| 275. #2561 | D89 | semidirect |
| 281. C89 | #9942 | semidirect |
| 314. C22×Q8 | C22⋊D89 | semidirect |
| 332. C2×C4⋊C4 | C22⋊D89 | semidirect |
| 346. C2×C42 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029510 | 2 |
| #26023571 | 2 |
| #26020197 | 2 |
| #26018785 | 2 |
| #26018579 | 2 |
| #26018105 | 2 |
| C89×#2561 | 2 |
| #9942 | 89 |