Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
384 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 3. C2×C4×#13063443 | C2 | semidirect |
| 4. #26012357 | C2 | semidirect |
| 7. C2×D173⋊C8 | C4 | semidirect |
| 11. #19149736 | C4 | semidirect |
| 33. #14583803 | C8 | semidirect |
| 40. #13063443 | C22⋊C4 | semidirect |
| 48. C2×Dic173 | C2×C8 | semidirect |
| 61. C2×C4×C173 | C2×C8 | semidirect |
| 71. C2×D173 | C4×C8 | semidirect |
| 84. C173 | C8×C22⋊C4 | semidirect |
| 143. C2×C4 | D173⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D173⋊C8 | 2 |
| C2×#19149736 | 2 |
| C2×C4×#13063443 | 2 |
| #26012357 | 2 |
| #26011338 | 2 |
| C8×C22⋊C4 | 173 |