Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
336 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 3. #26012345 | C2 | semidirect |
| 4. #26012344 | C2 | semidirect |
| 12. C2×Q8×D173 | C4 | semidirect |
| 15. #19149658 | C4 | semidirect |
| 20. C4⋊C4×D173 | C4 | semidirect |
| 22. C22⋊Q8×C173 | C4 | semidirect |
| 31. C2×Dic346 | C2×C4 | semidirect |
| 42. C4⋊Dic173 | C2×C4 | semidirect |
| 49. C2×Q8×C173 | C2×C4 | semidirect |
| 52. C4⋊C4×C173 | C2×C4 | semidirect |
| 113. D173 | #328 | semidirect |
| 114. C173 | C2×#328 | semidirect |
| 130. C22⋊Q8 | #10621924 | semidirect |
| 142. C2×Q8 | C2×#10621924 | semidirect |
| 164. C4⋊C4 | C2×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊(C22⋊C8) | 2 |
| C2×(C2×#10621924)⋊C4 | 2 |
| #26012345 | 2 |
| #26012344 | 2 |
| C22⋊Q8×D173 | 2 |
| C2×#328 | 173 |