Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
360 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 85 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×#15667951 | C2 | semidirect |
| 3. #26019014 | C2 | semidirect |
| 4. #26018214 | C2 | semidirect |
| 5. #26018213 | C2 | semidirect |
| 6. #26018212 | C2 | semidirect |
| 7. C89×#1331 | C2 | semidirect |
| 171. #1331 | D89 | semidirect |
| 172. C89 | #11675 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030828 | 2 |
| C4×#15667951 | 2 |
| #26019014 | 2 |
| #26018214 | 2 |
| #26018213 | 2 |
| #26018212 | 2 |
| C89×#1331 | 2 |
| #11675 | 89 |