Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
480 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26031045 | C2 | semidirect |
| 2. #26022181 | C2 | semidirect |
| 3. #26022164 | C2 | semidirect |
| 4. #26018263 | C2 | semidirect |
| 5. #26018260 | C2 | semidirect |
| 6. #26018176 | C2 | semidirect |
| 7. C89×#1999 | C2 | semidirect |
| 28. C2×Dic356 | D4 | semidirect |
| 30. C2×D712 | D4 | semidirect |
| 44. #15667946 | D4 | semidirect |
| 45. #15667946 | D4 | semidirect |
| 205. #1999 | D89 | semidirect |
| 209. C89 | #12104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031045 | 2 |
| #26022181 | 2 |
| #26022164 | 2 |
| #26018263 | 2 |
| #26018260 | 2 |
| #26018176 | 2 |
| C89×#1999 | 2 |
| #12104 | 89 |