Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
336 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 82 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. #26012345 | C2 | direct (N × H) |
| 14. #19149655 | C4 | semidirect |
| 16. C2×C4⋊Dic173 | C4 | semidirect |
| 19. C22×Q8×C173 | C4 | semidirect |
| 35. C4⋊Dic173 | C2×C4 | semidirect |
| 42. C2×Q8×C173 | C2×C4 | semidirect |
| 93. C2×C173 | #328 | semidirect |
| 100. C173 | C2×#328 | semidirect |
| 106. C22×Q8 | #10621924 | semidirect |
| 124. C2×Q8 | C2×#10621924 | semidirect |
| 197. C2 | #26012345 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149736 | 2 |
| C2×(C2×#10621924)⋊C4 | 2 |
| #26012345 | 2 |
| C2×#19149655 | 2 |
| C2×#328 | 173 |