Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
138 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 59 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. C4×#15667918 | C2 | semidirect |
| 3. C89×C4⋊C32 | C2 | semidirect |
| 43. D356 | C32 | semidirect |
| 66. C4⋊C32 | D89 | semidirect |
| 68. C89 | D4⋊C32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D356 | 2 |
| C4×#15667918 | 2 |
| C89×C4⋊C32 | 2 |
| D4⋊C32 | 89 |