Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
460 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26020241 | C2 | semidirect |
| 3. #26019007 | C2 | semidirect |
| 4. #26018703 | C2 | semidirect |
| 5. C2×#19151325 | C2 | semidirect |
| 6. #26018127 | C2 | semidirect |
| 7. C89×#1547 | C2 | semidirect |
| 204. #1547 | D89 | semidirect |
| 208. C89 | #10457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029712 | 2 |
| #26020241 | 2 |
| #26019007 | 2 |
| #26018703 | 2 |
| C2×#19151325 | 2 |
| #26018127 | 2 |
| C89×#1547 | 2 |
| #10457 | 89 |