Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
174 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 74 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. C2×D173⋊C16 | C2 | semidirect |
| 2. C4⋊#14583829 | C2 | semidirect |
| 3. #26012386 | C2 | semidirect |
| 4. C4×#14583829 | C2 | semidirect |
| 17. #14583829 | D4 | semidirect |
| 29. D692 | C16 | semidirect |
| 43. C2×D173 | C2×C16 | semidirect |
| 45. C4×C173 | C2×C16 | semidirect |
| 53. C173 | D4×C16 | semidirect |
| 100. C4 | D173⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D173⋊C16 | 2 |
| C4⋊#14583829 | 2 |
| #26012386 | 2 |
| C4×#14583829 | 2 |
| #26011556 | 2 |
| D4×C16 | 173 |