Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
604 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 604 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. C2×#19152033 | C2 | semidirect |
| 2. C2×#19151851 | C2 | semidirect |
| 3. C2×#19151408 | C2 | semidirect |
| 4. #26021967 | C2 | semidirect |
| 5. C2×#19151380 | C2 | semidirect |
| 6. #26018357 | C2 | semidirect |
| 7. C89×#3054 | C2 | semidirect |
| 38. C2×D712 | D4 | semidirect |
| 48. #15667952 | D4 | semidirect |
| 52. #15667944 | D4 | semidirect |
| 60. C2×Q16×C89 | D4 | semidirect |
| 62. C2×D8×C89 | D4 | semidirect |
| 77. #107×C89 | D4 | semidirect |
| 222. #3054 | D89 | semidirect |
| 228. C89 | #13316 | semidirect |
| 260. C2×Q16 | C22⋊D89 | semidirect |
| 268. C2×D8 | C22⋊D89 | semidirect |
| 295. #107 | 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 |
| C2×#19151851 | 2 |
| C2×#19151408 | 2 |
| #26021967 | 2 |
| C2×#19151380 | 2 |
| #26018357 | 2 |
| C89×#3054 | 2 |
| #13316 | 89 |