Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 217 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. #26011398 | C2 | semidirect |
| 4. #26011377 | C2 | semidirect |
| 5. #26011377 | C2 | semidirect |
| 7. C4⋊C4×Dic173 | C2 | semidirect |
| 28. C22⋊Q8×C173 | C4 | semidirect |
| 115. C173 | #2332 | semidirect |
| 128. C22⋊Q8 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011398 | 2 |
| #26011384 | 2 |
| #26011377 | 2 |
| #26011354 | 2 |
| C4⋊C4×Dic173 | 2 |
| C4×C22⋊Dic173 | 2 |
| C2×C22⋊Q8×C173 | 2 |
| #2332 | 173 |