Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
344 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26011969 | C2 | semidirect |
| 3. C2×#19149598 | C2 | semidirect |
| 4. #26011251 | C2 | semidirect |
| 15. #124×C173 | C4 | semidirect |
| 79. C173 | #1888 | semidirect |
| 90. #124 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011969 | 2 |
| #26011496 | 2 |
| C2×#19149598 | 2 |
| #26011251 | 2 |
| C2×#124×C173 | 2 |
| #1888 | 173 |