Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
194 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 59. Q8×C173 | Q16 | semidirect |
| 83. C173 | #1648 | semidirect |
| 139. Q8 | #14583816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011894 | 2 |
| #26011776 | 2 |
| #26011701 | 2 |
| #26011237 | 2 |
| Q8⋊#13063436 | 2 |
| #557×C173 | 2 |
| #1648 | 173 |