Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
600 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 269 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. #26011387 | C2 | semidirect |
| 5. #26011360 | C2 | semidirect |
| 6. #26011356 | C2 | semidirect |
| 9. #19149638 | C4 | semidirect |
| 29. C4⋊Dic173 | C2×C4 | semidirect |
| 34. C4×Dic173 | C2×C4 | semidirect |
| 62. C2×C4×C173 | C4⋊C4 | semidirect |
| 91. C173 | #2317 | semidirect |
| 154. C2×C4 | #14583805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149638 | 2 |
| #26011387 | 2 |
| #26011364 | 2 |
| #26011360 | 2 |
| #26011356 | 2 |
| C22×C4⋊C4×C173 | 2 |
| #2317 | 173 |