Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
522 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #26018085 | C2 | semidirect |
| 4. #26018080 | C2 | semidirect |
| 5. C89×#1276 | C2 | semidirect |
| 36. C42×D89 | C8 | semidirect |
| 153. #1276 | D89 | semidirect |
| 155. C89 | #8730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667969 | 2 |
| #26018564 | 2 |
| #26018085 | 2 |
| #26018080 | 2 |
| C89×#1276 | 2 |
| #8730 | 89 |