Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
568 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#19152033 | C2 | semidirect |
| 2. #26030739 | C2 | semidirect |
| 3. #26021988 | C2 | semidirect |
| 4. #26021969 | C2 | semidirect |
| 5. #26021151 | C2 | semidirect |
| 6. #26018337 | C2 | semidirect |
| 7. C89×#3414 | C2 | semidirect |
| 54. #15667952 | D4 | semidirect |
| 73. C2×Q16×C89 | D4 | semidirect |
| 77. C2×D8×C89 | D4 | semidirect |
| 85. C2×C16×C89 | D4 | semidirect |
| 218. #3414 | D89 | semidirect |
| 225. C89 | #13334 | semidirect |
| 265. C2×Q16 | C22⋊D89 | semidirect |
| 277. C2×D8 | C22⋊D89 | semidirect |
| 297. C2×C16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152033 | 2 |
| #26030739 | 2 |
| #26021988 | 2 |
| #26021969 | 2 |
| #26021151 | 2 |
| #26018337 | 2 |
| C89×#3414 | 2 |
| #13334 | 89 |