Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
566 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 566 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. C2×#19152038 | C2 | semidirect |
| 3. C2×#19151982 | C2 | semidirect |
| 4. C2×#19151413 | C2 | semidirect |
| 5. C2×#19151410 | C2 | semidirect |
| 6. #26018334 | C2 | semidirect |
| 7. C89×#1974 | C2 | semidirect |
| 204. #1974 | D89 | semidirect |
| 206. C89 | #13332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152038 | 2 |
| C2×#19152033 | 2 |
| C2×#19151982 | 2 |
| C2×#19151413 | 2 |
| C2×#19151410 | 2 |
| #26018334 | 2 |
| C89×#1974 | 2 |
| #13332 | 89 |