Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#15667955 | C2 | semidirect |
| 3. C2×#19151410 | C2 | semidirect |
| 4. #26021972 | C2 | semidirect |
| 5. C2×#19151382 | C2 | semidirect |
| 6. #26018349 | C2 | semidirect |
| 7. C2×#473×C89 | C2 | semidirect |
| 47. C2×#13083549 | D4 | semidirect |
| 61. C2×Q16×C89 | D4 | semidirect |
| 73. #108×C89 | D4 | semidirect |
| 196. C2×#473 | D89 | semidirect |
| 202. C89 | #13321 | semidirect |
| 235. C2×Q16 | C22⋊D89 | semidirect |
| 265. #108 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667955 | 2 |
| #26029900 | 2 |
| C2×#19151410 | 2 |
| #26021972 | 2 |
| C2×#19151382 | 2 |
| #26018349 | 2 |
| C2×#473×C89 | 2 |
| #13321 | 89 |