Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
480 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 480 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. C2×#19149679 | C2 | semidirect |
| 3. #26011782 | C2 | direct (N × H) |
| 4. C2×#19149611 | C2 | semidirect |
| 6. C2×C4⋊C8×C173 | C2 | semidirect |
| 11. #19149679 | C22 | semidirect |
| 18. #19149611 | C22 | semidirect |
| 22. C4⋊C8×C173 | C22 | semidirect |
| 28. C2×D692 | Q8 | semidirect |
| 54. D692 | C2×Q8 | semidirect |
| 85. C2×C173 | #476 | semidirect |
| 90. C173 | C2×#476 | semidirect |
| 96. C2×C4⋊C8 | D173 | semidirect |
| 112. C4⋊C8 | C2×D173 | semidirect |
| 177. C2 | #26011782 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149679 | 2 |
| C2×C4×D692 | 2 |
| #26011782 | 2 |
| C2×#19149611 | 2 |
| C2×#19149601 | 2 |
| C2×C4⋊C8×C173 | 2 |
| C2×#476 | 173 |