Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
618 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 147 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. #26018186 | C2 | direct (N × H) |
| 22. C22×Q8×C89 | C8 | semidirect |
| 51. C2×Q8×C89 | C2×C8 | semidirect |
| 139. C2×C89 | #1319 | semidirect |
| 146. C89 | C2×#1319 | semidirect |
| 162. C22×Q8 | #10623494 | semidirect |
| 192. C2×Q8 | C2×#10623494 | semidirect |
| 281. C2 | #26018186 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151324 | 2 |
| #26018186 | 2 |
| C2×#391×C89 | 2 |
| C2×#1319 | 89 |