Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
536 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 11. #19151393 | C4 | semidirect |
| 65. C2×Q8×C89 | C4⋊C4 | semidirect |
| 86. C42×C89 | C4⋊C4 | semidirect |
| 154. C89 | #12965 | semidirect |
| 201. C2×Q8 | #13083553 | semidirect |
| 235. C42 | #13083553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151393 | 2 |
| #26020641 | 2 |
| #26020532 | 2 |
| #26018370 | 2 |
| C89×#2372 | 2 |
| #12965 | 89 |