Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
516 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26029103 | C2 | semidirect |
| 3. C2×#19151410 | C2 | semidirect |
| 4. #26021967 | C2 | semidirect |
| 5. #26021160 | C2 | semidirect |
| 6. #26018340 | C2 | semidirect |
| 7. C89×#1382 | C2 | semidirect |
| 13. C2×D1424 | C4 | semidirect |
| 37. C2×D712 | C2×C4 | semidirect |
| 59. C2×C16×C89 | C2×C4 | semidirect |
| 171. #1382 | D89 | semidirect |
| 173. C89 | #13017 | semidirect |
| 220. C2×C16 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1424 | 2 |
| #26029103 | 2 |
| C2×#19151410 | 2 |
| #26021967 | 2 |
| #26021160 | 2 |
| #26018340 | 2 |
| C89×#1382 | 2 |
| #13017 | 89 |