Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
522 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26029053 | C2 | semidirect |
| 2. C2×#19151408 | C2 | semidirect |
| 3. #26021968 | C2 | semidirect |
| 4. #26021129 | C2 | semidirect |
| 5. #26018358 | C2 | semidirect |
| 6. #26018335 | C2 | semidirect |
| 24. #509×C89 | C4 | semidirect |
| 63. C2×D8×C89 | C2×C4 | semidirect |
| 69. M32×C89 | C2×C4 | semidirect |
| 106. Q16×C89 | C22⋊C4 | semidirect |
| 114. D8×C89 | C22⋊C4 | semidirect |
| 192. C89 | #13025 | semidirect |
| 197. #509 | Dic89 | semidirect |
| 226. C2×D8 | C2×Dic89 | semidirect |
| 244. M32 | C2×Dic89 | semidirect |
| 276. Q16 | C22⋊Dic89 | semidirect |
| 284. D8 | C22⋊Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029053 | 2 |
| C2×#19151408 | 2 |
| #26021968 | 2 |
| #26021129 | 2 |
| #26018358 | 2 |
| #26018335 | 2 |
| C2×#509×C89 | 2 |
| #13025 | 89 |