Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
448 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. C2×#19151380 | C2 | semidirect |
| 3. #26018239 | C2 | semidirect |
| 4. #26018236 | C2 | semidirect |
| 5. C2×H(3,ℤ/4)×C89 | C2 | semidirect |
| 6. C2×#15668034 | C4 | semidirect |
| 9. #19151856 | C4 | semidirect |
| 11. #19151851 | C4 | semidirect |
| 15. #19151636 | C4 | semidirect |
| 26. C2×Dic356 | C2×C4 | semidirect |
| 28. C2×D712 | C2×C4 | semidirect |
| 42. #15667944 | C2×C4 | semidirect |
| 43. #15667944 | C2×C4 | semidirect |
| 195. C2×H(3,ℤ/4) | D89 | semidirect |
| 198. C89 | #11685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029861 | 2 |
| C2×#19151380 | 2 |
| #26018239 | 2 |
| #26018236 | 2 |
| C2×H(3,ℤ/4)×C89 | 2 |
| #11685 | 89 |