Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
524 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 237 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 |
|---|---|---|
| 2. #26011377 | C2 | semidirect |
| 3. C4×C4⋊Dic173 | C2 | semidirect |
| 5. #26011337 | C2 | semidirect |
| 6. C42×Dic173 | C2 | semidirect |
| 17. #117×C173 | C4 | semidirect |
| 75. C173 | #2298 | semidirect |
| 85. #117 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011384 | 2 |
| #26011377 | 2 |
| C4×C4⋊Dic173 | 2 |
| C4×C22⋊Dic173 | 2 |
| #26011337 | 2 |
| C42×Dic173 | 2 |
| C2×#117×C173 | 2 |
| #2298 | 173 |