Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
402 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 73 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. #26021099 | C2 | semidirect |
| 3. #26019017 | C2 | semidirect |
| 4. #26018851 | C2 | semidirect |
| 5. #26018844 | C2 | semidirect |
| 6. #26018125 | C2 | semidirect |
| 7. C89×#1557 | C2 | semidirect |
| 192. #1557 | D89 | semidirect |
| 196. C89 | #10496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031235 | 2 |
| #26021099 | 2 |
| #26019017 | 2 |
| #26018851 | 2 |
| #26018844 | 2 |
| #26018125 | 2 |
| C89×#1557 | 2 |
| #10496 | 89 |