Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
822 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 1. #26023317 | C2 | semidirect |
| 2. #26021180 | C2 | semidirect |
| 3. C2×#19151342 | C2 | semidirect |
| 4. #26018092 | C2 | semidirect |
| 18. #493×C89 | C4 | semidirect |
| 46. #127×C89 | C2×C4 | semidirect |
| 50. C4×C8×C89 | C2×C4 | semidirect |
| 61. C4⋊Dic89 | D8 | semidirect |
| 175. C89 | #9061 | semidirect |
| 181. #493 | Dic89 | semidirect |
| 204. #127 | C2×Dic89 | semidirect |
| 219. C4×C8 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023317 | 2 |
| #26021180 | 2 |
| C2×#19151342 | 2 |
| #26018092 | 2 |
| C2×#493×C89 | 2 |
| #9061 | 89 |