Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
692 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#19151912 | C2 | semidirect |
| 3. #26024723 | C2 | semidirect |
| 4. #26021088 | C2 | semidirect |
| 5. #26020339 | C2 | semidirect |
| 6. #26018821 | C2 | semidirect |
| 7. C89×#1282 | C2 | semidirect |
| 133. C22⋊C4×C89 | D8 | semidirect |
| 233. #1282 | D89 | semidirect |
| 234. C89 | #9952 | semidirect |
| 360. C22⋊C4 | D712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031003 | 2 |
| C2×#19151912 | 2 |
| #26024723 | 2 |
| #26021088 | 2 |
| #26020339 | 2 |
| #26018821 | 2 |
| C89×#1282 | 2 |
| #9952 | 89 |