Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
172 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 16. #19149590 | C4 | semidirect |
| 17. C4×#13063436 | C4 | semidirect |
| 78. C173 | #1833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149614 | 2 |
| #26011527 | 2 |
| #26011447 | 2 |
| #26011263 | 2 |
| #26011261 | 2 |
| #26011247 | 2 |
| H(3,ℤ/4)×C173 | 2 |
| #1833 | 173 |