Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 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×#19151865 | C2 | semidirect |
| 2. #26029918 | C2 | semidirect |
| 3. C2×#19151405 | C2 | semidirect |
| 4. C2×#19151399 | C2 | semidirect |
| 5. C2×#19151383 | C2 | semidirect |
| 6. #26018361 | C2 | semidirect |
| 7. C2×#509×C89 | C2 | semidirect |
| 54. #15667948 | D4 | semidirect |
| 74. C2×D8×C89 | D4 | semidirect |
| 79. M32×C89 | D4 | semidirect |
| 219. C2×#509 | D89 | semidirect |
| 226. C89 | #13307 | semidirect |
| 269. C2×D8 | C22⋊D89 | semidirect |
| 288. M32 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151865 | 2 |
| #26029918 | 2 |
| C2×#19151405 | 2 |
| C2×#19151399 | 2 |
| C2×#19151383 | 2 |
| #26018361 | 2 |
| C2×#509×C89 | 2 |
| #13307 | 89 |