Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
462 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 111 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. #346×D89 | C2 | semidirect |
| 3. #334×D89 | C2 | semidirect |
| 4. #26018220 | C2 | semidirect |
| 5. #26018219 | C2 | semidirect |
| 6. #26018218 | C2 | semidirect |
| 7. C89×#1333 | C2 | semidirect |
| 20. #19151374 | C22 | semidirect |
| 22. #19151349 | C22 | semidirect |
| 25. #346×C89 | C22 | semidirect |
| 26. #334×C89 | C22 | semidirect |
| 32. D8×D89 | C8 | semidirect |
| 77. D712 | C2×C8 | semidirect |
| 98. D8×C89 | C2×C8 | semidirect |
| 167. D89 | #1333 | direct (N × H) |
| 174. #1333 | D89 | direct (N × H) |
| 175. C89 | C2×#1333 | semidirect |
| 191. #346 | C2×D89 | semidirect |
| 194. #334 | C2×D89 | semidirect |
| 250. D8 | C8×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×D89 | 2 |
| #346×D89 | 2 |
| #334×D89 | 2 |
| #26018220 | 2 |
| #26018219 | 2 |
| #26018218 | 2 |
| C89×#1333 | 2 |
| C2×#1333 | 89 |