Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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. #26011871 | C2 | semidirect |
| 4. #26011842 | C2 | semidirect |
| 5. #26011702 | C2 | semidirect |
| 67. C2×C4×C173 | Q16 | semidirect |
| 92. C173 | #3209 | semidirect |
| 160. C2×C4 | Dic692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012048 | 2 |
| C2×#19149679 | 2 |
| #26011871 | 2 |
| #26011842 | 2 |
| #26011702 | 2 |
| #26011649 | 2 |
| #431×C173 | 2 |
| #3209 | 173 |