Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
536 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 101 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. C4×#15668018 | C2 | semidirect |
| 3. #26018844 | C2 | semidirect |
| 4. #26018689 | C2 | semidirect |
| 5. #26018141 | C2 | semidirect |
| 6. #26018089 | C2 | semidirect |
| 7. C89×#1492 | C2 | semidirect |
| 216. #1492 | D89 | semidirect |
| 220. C89 | #9211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030306 | 2 |
| C4×#15668018 | 2 |
| #26018844 | 2 |
| #26018689 | 2 |
| #26018141 | 2 |
| #26018089 | 2 |
| C89×#1492 | 2 |
| #9211 | 89 |