Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
750 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 750 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#19151737 | C2 | semidirect |
| 3. #26020176 | C2 | semidirect |
| 4. #26018612 | C2 | semidirect |
| 5. #26018611 | C2 | semidirect |
| 6. #26018140 | C2 | semidirect |
| 7. C2×#448×C89 | C2 | semidirect |
| 227. C2×#448 | D89 | semidirect |
| 232. C89 | #9988 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031049 | 2 |
| C2×#19151737 | 2 |
| #26020176 | 2 |
| #26018612 | 2 |
| #26018611 | 2 |
| #26018140 | 2 |
| C2×#448×C89 | 2 |
| #9988 | 89 |