Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
584 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×#14583815 | C2 | semidirect |
| 3. C2×C4×Dic346 | C2 | semidirect |
| 4. #26011692 | C2 | direct (N × H) |
| 5. C2×#19149601 | C2 | semidirect |
| 6. C2×C4⋊C8×C173 | C2 | semidirect |
| 12. C2×#14583815 | C22 | semidirect |
| 16. C4×Dic346 | C22 | semidirect |
| 20. #19149601 | C22 | semidirect |
| 23. C4⋊C8×C173 | C22 | semidirect |
| 27. C2×Dic346 | D4 | semidirect |
| 57. Dic346 | C2×D4 | semidirect |
| 69. C2×C4×C173 | SD16 | semidirect |
| 87. C4×C173 | C2×SD16 | semidirect |
| 92. C2×C173 | #460 | semidirect |
| 97. C173 | C2×#460 | semidirect |
| 103. C2×C4⋊C8 | D173 | semidirect |
| 120. C4⋊C8 | C2×D173 | semidirect |
| 167. C2×C4 | #14583815 | semidirect |
| 187. C4 | C2×#14583815 | semidirect |
| 191. C2 | #26011692 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583815 | 2 |
| C2×#19149676 | 2 |
| C2×C4×Dic346 | 2 |
| #26011692 | 2 |
| C2×#19149601 | 2 |
| C2×C4⋊C8×C173 | 2 |
| C2×#460 | 173 |