Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
262 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26011251 | C2 | semidirect |
| 4. #26011247 | C2 | semidirect |
| 15. #117×C173 | C4 | semidirect |
| 17. C2×C42×C173 | C4 | semidirect |
| 79. C173 | #1827 | semidirect |
| 92. #117 | Dic173 | semidirect |
| 94. C2×C42 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011475 | 2 |
| #26011465 | 2 |
| #26011251 | 2 |
| #26011247 | 2 |
| C4×#41×C173 | 2 |
| #1827 | 173 |