Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
780 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 97 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×#19151985 | C2 | semidirect |
| 2. #26028297 | C2 | semidirect |
| 3. #26021077 | C2 | semidirect |
| 4. C2×#19151338 | C2 | semidirect |
| 5. C2×#19151337 | C2 | semidirect |
| 6. #26018134 | C2 | semidirect |
| 7. C2×#496×C89 | C2 | semidirect |
| 53. #15667923 | D4 | semidirect |
| 70. #127×C89 | D4 | semidirect |
| 79. #97×C89 | D4 | semidirect |
| 234. C2×#496 | D89 | semidirect |
| 240. C89 | #10078 | semidirect |
| 286. #127 | C22⋊D89 | semidirect |
| 309. #97 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151985 | 2 |
| #26028297 | 2 |
| #26021077 | 2 |
| C2×#19151338 | 2 |
| C2×#19151337 | 2 |
| #26018134 | 2 |
| C2×#496×C89 | 2 |
| #10078 | 89 |