Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
148 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 10. #19149625 | C4 | semidirect |
| 63. C173 | #2176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149625 | 2 |
| C4×Dic692 | 2 |
| #26011318 | 2 |
| #26011295 | 2 |
| #26011294 | 2 |
| #26011267 | 2 |
| C4×Q16×C173 | 2 |
| #2176 | 173 |