Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
398 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26022169 | C2 | semidirect |
| 3. #26018260 | C2 | semidirect |
| 4. #26018192 | C2 | semidirect |
| 5. C89×#2056 | C2 | semidirect |
| 100. C2×C4×C89 | SD32 | semidirect |
| 139. #2056 | D89 | semidirect |
| 142. C89 | #12161 | semidirect |
| 246. C2×C4 | #15667955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031562 | 2 |
| #26022169 | 2 |
| #26018260 | 2 |
| #26018192 | 2 |
| C89×#2056 | 2 |
| #12161 | 89 |