Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
966 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 966 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26023072 | C2 | semidirect |
| 3. #26021087 | C2 | semidirect |
| 4. #26020182 | C2 | semidirect |
| 5. #26018819 | C2 | semidirect |
| 6. #26018099 | C2 | semidirect |
| 7. C89×#1289 | C2 | semidirect |
| 9. C22×D712 | C4 | semidirect |
| 16. C2×#15667934 | C4 | semidirect |
| 35. C22×D356 | C2×C4 | semidirect |
| 50. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 69. C22×C8×C89 | C2×C4 | semidirect |
| 128. C22⋊Dic89 | D8 | semidirect |
| 227. D356 | #99 | semidirect |
| 294. #1289 | D89 | semidirect |
| 296. C89 | #9259 | semidirect |
| 335. C22×C8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151734 | 2 |
| #26023072 | 2 |
| #26021087 | 2 |
| #26020182 | 2 |
| #26018819 | 2 |
| #26018099 | 2 |
| C89×#1289 | 2 |
| #9259 | 89 |