Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
522 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26029053 | C2 | semidirect |
| 3. #26021969 | C2 | semidirect |
| 4. #26021126 | C2 | semidirect |
| 5. #26018359 | C2 | semidirect |
| 6. #26018335 | C2 | semidirect |
| 7. C2×#360×C89 | C2 | semidirect |
| 11. #19152033 | C4 | semidirect |
| 34. C2×D712 | C2×C4 | semidirect |
| 47. #15667952 | C2×C4 | semidirect |
| 108. Q16×C89 | C22⋊C4 | semidirect |
| 112. D8×C89 | C22⋊C4 | semidirect |
| 187. C2×#360 | D89 | semidirect |
| 192. C89 | #13025 | semidirect |
| 276. Q16 | #13083551 | semidirect |
| 284. D8 | #13083551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152033 | 2 |
| #26029053 | 2 |
| #26021969 | 2 |
| #26021126 | 2 |
| #26018359 | 2 |
| #26018335 | 2 |
| C2×#360×C89 | 2 |
| #13025 | 89 |