Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
292 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 12. C4⋊Q8×C173 | C4 | semidirect |
| 20. C4⋊Dic173 | Q8 | semidirect |
| 69. C173 | #1988 | semidirect |
| 78. C4⋊Q8 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#13063436 | 2 |
| C4×C4⋊Dic173 | 2 |
| #26011253 | 2 |
| C2×C4⋊Q8×C173 | 2 |
| #1988 | 173 |