Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
130 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 30. Q16×C173 | Q8 | semidirect |
| 59. C173 | #2227 | semidirect |
| 82. Q16 | Dic346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011895 | 2 |
| Q16×Dic173 | 2 |
| #26011317 | 2 |
| #26011316 | 2 |
| #26011309 | 2 |
| #26011295 | 2 |
| #358×C173 | 2 |
| #2227 | 173 |