Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
296 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 9. C4×#13063443 | C4 | semidirect |
| 10. C4×#13063443 | C4 | semidirect |
| 13. C4×#13063436 | C4 | semidirect |
| 14. C8×Dic173 | C4 | semidirect |
| 15. C4×C8×C173 | C4 | semidirect |
| 21. C4×#10621924 | C8 | semidirect |
| 63. C173 | #1744 | semidirect |
| 79. C4×C8 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D173⋊C8 | 2 |
| C42×#10621924 | 2 |
| (C2×#10621924)⋊C8 | 2 |
| C4×C8×D173 | 2 |
| #1744 | 173 |