Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
474 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26019013 | C2 | semidirect |
| 3. #26018849 | C2 | semidirect |
| 4. #26018605 | C2 | semidirect |
| 5. #26018604 | C2 | semidirect |
| 6. #26018539 | C2 | semidirect |
| 7. C89×#1527 | C2 | semidirect |
| 206. #1527 | D89 | semidirect |
| 210. C89 | #9791 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151980 | 2 |
| #26019013 | 2 |
| #26018849 | 2 |
| #26018605 | 2 |
| #26018604 | 2 |
| #26018539 | 2 |
| C89×#1527 | 2 |
| #9791 | 89 |