Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
712 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 183 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 |
|---|---|---|
| 73. C2×Q8×C89 | Q16 | semidirect |
| 144. C89 | #32670 | semidirect |
| 202. C2×Q8 | Dic356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025464 | 2 |
| #26021575 | 2 |
| #26021354 | 2 |
| #26021113 | 2 |
| #26020894 | 2 |
| C89×#1984 | 2 |
| #32670 | 89 |