Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1202 conjugacy classes of subgroups; only the 355 normal subgroups are shown.
This group has 1202 conjugacy classes of subgroups — too many to draw. Only its 355 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. #26029333 | C2 | semidirect |
| 3. #26018811 | C2 | semidirect |
| 4. #26018746 | C2 | semidirect |
| 5. C89×#2351 | C2 | semidirect |
| 7. #19152270 | C4 | semidirect |
| 8. Q8×D356 | C4 | semidirect |
| 129. #2351 | D89 | semidirect |
| 132. C89 | #17618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034023 | 2 |
| #26029333 | 2 |
| #26018811 | 2 |
| #26018746 | 2 |
| C89×#2351 | 2 |
| #17618 | 89 |