Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
300 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 70 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×#19149750 | C2 | semidirect |
| 2. C2×#19149744 | C2 | semidirect |
| 3. #26012466 | C2 | semidirect |
| 4. C2×C8×#10621924 | C2 | semidirect |
| 16. C2×#14583813 | C4 | semidirect |
| 17. C2×D1384 | C4 | semidirect |
| 19. C2×Q16×C173 | C4 | semidirect |
| 85. C173 | #1974 | semidirect |
| 95. C2×Q16 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149750 | 2 |
| C2×#19149744 | 2 |
| #26012466 | 2 |
| C2×C8×#10621924 | 2 |
| C2×#19149702 | 2 |
| #1974 | 173 |