Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
364 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 1. #26011622 | C2 | semidirect |
| 2. Q8×#13063436 | C2 | semidirect |
| 25. C2×#13063436 | Q8 | semidirect |
| 67. C173 | #2960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011622 | 2 |
| Q8×#13063436 | 2 |
| #26011518 | 2 |
| #26011515 | 2 |
| #26011447 | 2 |
| C2×C4×#13063436 | 2 |
| #533×C173 | 2 |
| #2960 | 173 |