Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
450 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 75 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×#19151397 | C2 | semidirect |
| 3. #26018418 | C2 | direct (N × H) |
| 4. C2×#356×C89 | C2 | semidirect |
| 15. #19151397 | C22 | semidirect |
| 19. #356×C89 | C22 | semidirect |
| 149. C2×C89 | #1410 | semidirect |
| 154. C2×#356 | D89 | semidirect |
| 156. C89 | C2×#1410 | semidirect |
| 171. #356 | C2×D89 | semidirect |
| 301. C2 | #26018418 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151972 | 2 |
| C2×#19151397 | 2 |
| #26018418 | 2 |
| C2×#356×C89 | 2 |
| C2×#1410 | 89 |