Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
378 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 378 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. C4×C16×D89 | C2 | semidirect |
| 3. #26019009 | C2 | semidirect |
| 4. #26018214 | C2 | semidirect |
| 5. #26018213 | C2 | semidirect |
| 6. #26018212 | C2 | semidirect |
| 7. C89×#1331 | C2 | semidirect |
| 172. #1331 | D89 | semidirect |
| 173. C89 | #11671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030828 | 2 |
| C4×C16×D89 | 2 |
| #26019009 | 2 |
| #26018214 | 2 |
| #26018213 | 2 |
| #26018212 | 2 |
| C89×#1331 | 2 |
| #11671 | 89 |