Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
480 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26031046 | C2 | semidirect |
| 2. #26022164 | C2 | semidirect |
| 3. #26021247 | C2 | semidirect |
| 4. #26018264 | C2 | semidirect |
| 5. #26018262 | C2 | semidirect |
| 6. #26018175 | C2 | semidirect |
| 7. C89×#2187 | C2 | semidirect |
| 31. C2×D712 | D4 | semidirect |
| 47. #15667946 | D4 | semidirect |
| 56. C2×Q16×C89 | D4 | semidirect |
| 64. #107×C89 | D4 | semidirect |
| 203. #2187 | D89 | semidirect |
| 209. C89 | #12104 | semidirect |
| 233. C2×Q16 | C22⋊D89 | semidirect |
| 259. #107 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031046 | 2 |
| #26022164 | 2 |
| #26021247 | 2 |
| #26018264 | 2 |
| #26018262 | 2 |
| #26018175 | 2 |
| C89×#2187 | 2 |
| #12104 | 89 |