Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
742 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 742 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 |
|---|---|---|
| 1. #26023019 | C2 | semidirect |
| 2. #26020196 | C2 | semidirect |
| 3. #26020170 | C2 | semidirect |
| 4. #26018781 | C2 | semidirect |
| 5. #26018161 | C2 | semidirect |
| 6. #26018106 | C2 | semidirect |
| 27. #448×C89 | C4 | semidirect |
| 28. #447×C89 | C4 | semidirect |
| 63. C22×Q8×C89 | C2×C4 | semidirect |
| 66. C22×D4×C89 | C2×C4 | semidirect |
| 84. C22⋊C8×C89 | C2×C4 | semidirect |
| 294. C89 | #9523 | semidirect |
| 299. #448 | Dic89 | semidirect |
| 300. #447 | Dic89 | semidirect |
| 324. C22×Q8 | C2×Dic89 | semidirect |
| 327. C22×D4 | C2×Dic89 | semidirect |
| 364. C22⋊C8 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023019 | 2 |
| #26020196 | 2 |
| #26020170 | 2 |
| #26018781 | 2 |
| #26018161 | 2 |
| #26018106 | 2 |
| C89×#3006 | 2 |
| #9523 | 89 |