Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
162 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26018322 | C2 | semidirect |
| 3. C8×C16×C89 | C2 | semidirect |
| 26. D712 | C16 | semidirect |
| 74. C8×C16 | D89 | semidirect |
| 75. C89 | #7068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×D712 | 2 |
| #26018322 | 2 |
| C8×C16×C89 | 2 |
| #7068 | 89 |