Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
924 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26021236 | C2 | semidirect |
| 5. #26018823 | C2 | semidirect |
| 6. #26018099 | C2 | semidirect |
| 7. C89×#1289 | C2 | semidirect |
| 9. C22×#13083563 | C4 | semidirect |
| 16. C2×#15667934 | C4 | semidirect |
| 30. C22×Dic178 | C2×C4 | semidirect |
| 49. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 67. C22×C8×C89 | C2×C4 | semidirect |
| 124. C22⋊Dic89 | SD16 | semidirect |
| 275. #1289 | D89 | semidirect |
| 277. C89 | #9255 | semidirect |
| 315. C22×C8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151751 | 2 |
| #26023072 | 2 |
| #26021236 | 2 |
| #26020182 | 2 |
| #26018823 | 2 |
| #26018099 | 2 |
| C89×#1289 | 2 |
| #9255 | 89 |