Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
372 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26018279 | C2 | semidirect |
| 4. #26018198 | C2 | semidirect |
| 5. C89×#2571 | C2 | semidirect |
| 129. #2571 | D89 | semidirect |
| 134. C89 | #12181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021476 | 2 |
| #26019288 | 2 |
| #26018279 | 2 |
| #26018198 | 2 |
| C89×#2571 | 2 |
| #12181 | 89 |