Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
588 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 1. #26028245 | C2 | semidirect |
| 4. #26018077 | C2 | semidirect |
| 5. C89×#1272 | C2 | semidirect |
| 52. C2×Dic178 | SD16 | semidirect |
| 79. C2×Q8×C89 | SD16 | semidirect |
| 158. #1272 | D89 | semidirect |
| 159. C89 | #7749 | semidirect |
| 210. C2×Q8 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028245 | 2 |
| #26021342 | 2 |
| #26021339 | 2 |
| #26018077 | 2 |
| C89×#1272 | 2 |
| #7749 | 89 |