Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
264 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 7. C22⋊#13063443 | C4 | semidirect |
| 12. C22⋊#13063436 | C4 | semidirect |
| 14. C22⋊C8×C173 | C4 | semidirect |
| 19. C22×#10621924 | C8 | semidirect |
| 88. C173 | #1280 | semidirect |
| 101. C22⋊C8 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊(C22⋊C8) | 2 |
| C2×(C2×#10621924)⋊C4 | 2 |
| C22⋊C8×D173 | 2 |
| #1280 | 173 |