Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
628 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 389 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 |
|---|---|---|
| 6. Q8×Dic173 | C4 | semidirect |
| 14. C4×Q8×C173 | C4 | semidirect |
| 36. Q8×C173 | C42 | semidirect |
| 59. C173 | #2276 | semidirect |
| 68. C4×Q8 | Dic173 | semidirect |
| 90. Q8 | C4×Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic173 | 2 |
| C4⋊C4×Dic173 | 2 |
| C4×C4⋊Dic173 | 2 |
| #26011337 | 2 |
| C2×C4×Q8×C173 | 2 |
| #2276 | 173 |