Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
534 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26021238 | C2 | semidirect |
| 3. #26018785 | C2 | semidirect |
| 5. #26018159 | C2 | semidirect |
| 6. #26018106 | C2 | semidirect |
| 26. #480×C89 | C4 | semidirect |
| 29. #448×C89 | C4 | semidirect |
| 53. C22×Q8×C89 | C2×C4 | semidirect |
| 68. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 76. C22⋊C8×C89 | C2×C4 | semidirect |
| 237. C89 | #9341 | semidirect |
| 241. #480 | Dic89 | semidirect |
| 244. #448 | Dic89 | semidirect |
| 261. C22×Q8 | C2×Dic89 | semidirect |
| 280. C2×C4⋊C4 | C2×Dic89 | semidirect |
| 299. C22⋊C8 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023409 | 2 |
| #26021238 | 2 |
| #26018785 | 2 |
| #26018768 | 2 |
| #26018159 | 2 |
| #26018106 | 2 |
| C89×#3193 | 2 |
| #9341 | 89 |