Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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. M16×Dic173 | C2 | semidirect |
| 4. #26011260 | C2 | semidirect |
| 5. #343×C173 | C2 | semidirect |
| 13. #19149595 | C4 | semidirect |
| 29. #14583810 | C2×C4 | semidirect |
| 37. M16×C173 | C2×C4 | semidirect |
| 78. Dic173 | #100 | semidirect |
| 85. C173 | C4×#100 | semidirect |
| 91. #343 | D173 | semidirect |
| 119. M16 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149641 | 2 |
| C2×#19149595 | 2 |
| M16×Dic173 | 2 |
| #26011260 | 2 |
| #343×C173 | 2 |
| C4×#100 | 173 |