Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
688 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 189 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×#19149662 | C2 | semidirect |
| 3. #26011393 | C2 | semidirect |
| 4. #26011389 | C2 | semidirect |
| 5. #26011382 | C2 | semidirect |
| 6. #26011370 | C2 | semidirect |
| 7. #26011351 | C2 | semidirect |
| 8. C22×C42×C173 | C2 | semidirect |
| 50. C22×C4×C173 | D4 | semidirect |
| 107. C4×C173 | #123 | semidirect |
| 117. C173 | #2854 | semidirect |
| 121. C22×C42 | D173 | semidirect |
| 161. C22×C4 | D692 | semidirect |
| 227. C4 | #19149662 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149662 | 2 |
| C2×#19149653 | 2 |
| #26011393 | 2 |
| #26011389 | 2 |
| #26011382 | 2 |
| #26011370 | 2 |
| #26011351 | 2 |
| C22×C42×C173 | 2 |
| #2854 | 173 |