Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
692 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#19151909 | C2 | semidirect |
| 2. #26024724 | C2 | semidirect |
| 3. #26021089 | C2 | semidirect |
| 4. #26020339 | C2 | semidirect |
| 5. #26018820 | C2 | semidirect |
| 6. #26018099 | C2 | semidirect |
| 96. C22⋊Dic89 | D8 | semidirect |
| 234. C89 | #9952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151909 | 2 |
| #26024724 | 2 |
| #26021089 | 2 |
| #26020339 | 2 |
| #26018820 | 2 |
| #26018099 | 2 |
| C89×#3186 | 2 |
| #9952 | 89 |