Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
588 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 588 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 |
|---|---|---|
| 11. #19149677 | C4 | semidirect |
| 48. C4×Dic173 | Q8 | semidirect |
| 96. Dic173 | C4×Q8 | semidirect |
| 97. Dic173 | C4⋊Q8 | semidirect |
| 103. C173 | C4×C4⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149677 | 2 |
| C2×Q8×Dic173 | 2 |
| C2×#19149644 | 2 |
| #26011397 | 2 |
| #26011388 | 2 |
| #26011360 | 2 |
| #26011342 | 2 |
| C42×Dic173 | 2 |
| #391×C173 | 2 |
| C4×C4⋊Q8 | 173 |