Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
272 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26011548 | C2 | semidirect |
| 2. #26011337 | C2 | semidirect |
| 3. #26011225 | C2 | semidirect |
| 12. C4⋊Q8×C173 | C4 | semidirect |
| 13. #127×C173 | C4 | semidirect |
| 18. C4×D4×C173 | C4 | semidirect |
| 83. C173 | #1505 | semidirect |
| 90. C4⋊Q8 | Dic173 | semidirect |
| 91. #127 | Dic173 | semidirect |
| 96. C4×D4 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011548 | 2 |
| #26011337 | 2 |
| #26011225 | 2 |
| #532×C173 | 2 |
| #1505 | 173 |