Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
762 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26022865 | C2 | semidirect |
| 3. #26018820 | C2 | semidirect |
| 4. C2×#19151321 | C2 | semidirect |
| 5. #26018120 | C2 | semidirect |
| 6. #26018119 | C2 | semidirect |
| 7. C89×#1519 | C2 | semidirect |
| 12. #19151524 | C4 | semidirect |
| 14. #19151506 | C4 | semidirect |
| 54. #15667919 | C2×C4 | semidirect |
| 55. #15667919 | D4 | semidirect |
| 57. C22×D4×C89 | C2×C4 | semidirect |
| 65. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 70. #95×C89 | D4 | semidirect |
| 259. #1519 | D89 | semidirect |
| 263. C89 | #9203 | semidirect |
| 286. C22×D4 | C4×D89 | semidirect |
| 302. C2×C4⋊C4 | C4×D89 | semidirect |
| 326. #95 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025988 | 2 |
| #26022865 | 2 |
| #26018820 | 2 |
| C2×#19151321 | 2 |
| #26018120 | 2 |
| #26018119 | 2 |
| C89×#1519 | 2 |
| #9203 | 89 |