Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
604 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26029857 | C2 | semidirect |
| 2. C2×#19151848 | C2 | semidirect |
| 3. C2×#19151408 | C2 | semidirect |
| 4. #26021968 | C2 | semidirect |
| 5. C2×#19151379 | C2 | semidirect |
| 6. #26018358 | C2 | semidirect |
| 7. C2×#509×C89 | C2 | semidirect |
| 53. #15667946 | D4 | semidirect |
| 56. #15667944 | D4 | semidirect |
| 66. C2×Q16×C89 | D4 | semidirect |
| 73. C2×D8×C89 | D4 | semidirect |
| 74. C2×D8×C89 | D4 | semidirect |
| 79. M32×C89 | D4 | semidirect |
| 221. C2×#509 | D89 | semidirect |
| 228. C89 | #13316 | semidirect |
| 260. C2×Q16 | C22⋊D89 | semidirect |
| 267. C2×D8 | C22⋊D89 | semidirect |
| 268. C2×D8 | C22⋊D89 | semidirect |
| 292. M32 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029857 | 2 |
| C2×#19151848 | 2 |
| C2×#19151408 | 2 |
| #26021968 | 2 |
| C2×#19151379 | 2 |
| #26018358 | 2 |
| C2×#509×C89 | 2 |
| #13316 | 89 |