Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
442 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 2. #26022508 | C2 | semidirect |
| 3. #26022298 | C2 | semidirect |
| 4. #26019617 | C2 | semidirect |
| 5. #26018299 | C2 | semidirect |
| 6. #26018214 | C2 | semidirect |
| 7. C89×D4⋊C16 | C2 | semidirect |
| 12. #19151978 | C22 | semidirect |
| 20. #19151351 | C22 | semidirect |
| 23. C4⋊C16×C89 | C22 | semidirect |
| 24. C4×C16×C89 | C22 | semidirect |
| 103. D4×C89 | SD32 | semidirect |
| 162. D4⋊C16 | D89 | semidirect |
| 163. C89 | #12320 | semidirect |
| 176. C4⋊C16 | C2×D89 | semidirect |
| 178. C4×C16 | C2×D89 | semidirect |
| 270. D4 | #15667957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D712 | 2 |
| #26022508 | 2 |
| #26022298 | 2 |
| #26019617 | 2 |
| #26018299 | 2 |
| #26018214 | 2 |
| C89×D4⋊C16 | 2 |
| #12320 | 89 |