Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
518 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 91 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. #349×D89 | C2 | semidirect |
| 3. #26018190 | C2 | semidirect |
| 4. #26018189 | C2 | semidirect |
| 5. C89×#1321 | C2 | semidirect |
| 15. #19151380 | C22 | semidirect |
| 18. #349×C89 | C22 | semidirect |
| 206. D89 | #1321 | direct (N × H) |
| 211. #1321 | D89 | direct (N × H) |
| 212. C89 | C2×#1321 | semidirect |
| 225. #349 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #408×D89 | 2 |
| #349×D89 | 2 |
| #26018190 | 2 |
| #26018189 | 2 |
| C89×#1321 | 2 |
| C2×#1321 | 89 |