Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
420 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. #26018283 | C2 | semidirect |
| 5. #26018281 | C2 | semidirect |
| 6. #26018258 | C2 | semidirect |
| 7. C89×#1346 | C2 | semidirect |
| 197. #1346 | D89 | semidirect |
| 198. C89 | #11739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026177 | 2 |
| #26020043 | 2 |
| #26018569 | 2 |
| #26018283 | 2 |
| #26018281 | 2 |
| #26018258 | 2 |
| C89×#1346 | 2 |
| #11739 | 89 |