Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
426 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 59 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. #26022202 | C2 | semidirect |
| 2. #26022197 | C2 | semidirect |
| 3. #26021319 | C2 | semidirect |
| 4. #26018240 | C2 | semidirect |
| 5. #26018237 | C2 | semidirect |
| 6. #26018188 | C2 | semidirect |
| 7. C89×#3197 | C2 | semidirect |
| 47. C2×Q16×C89 | D4 | semidirect |
| 49. C2×D8×C89 | D4 | semidirect |
| 62. #106×C89 | D4 | semidirect |
| 63. #106×C89 | D4 | semidirect |
| 195. #3197 | D89 | semidirect |
| 202. C89 | #12116 | semidirect |
| 229. C2×Q16 | C22⋊D89 | semidirect |
| 231. C2×D8 | C22⋊D89 | semidirect |
| 256. #106 | C22⋊D89 | semidirect |
| 257. #106 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022202 | 2 |
| #26022197 | 2 |
| #26021319 | 2 |
| #26018240 | 2 |
| #26018237 | 2 |
| #26018188 | 2 |
| C89×#3197 | 2 |
| #12116 | 89 |