Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
702 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#101×D89 | C2 | semidirect |
| 3. C2×#19151394 | C2 | semidirect |
| 4. C2×#19151394 | C2 | semidirect |
| 5. #26020174 | C2 | semidirect |
| 6. #26018379 | C2 | semidirect |
| 7. C89×#1394 | C2 | semidirect |
| 69. #15667931 | D4 | semidirect |
| 85. #101×C89 | D4 | semidirect |
| 261. C2×D89 | #355 | semidirect |
| 289. #1394 | D89 | semidirect |
| 290. C89 | #13092 | semidirect |
| 363. #101 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#101×D89 | 2 |
| #26023909 | 2 |
| C2×#19151394 | 2 |
| #26020174 | 2 |
| #26018379 | 2 |
| C89×#1394 | 2 |
| #13092 | 89 |