Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
600 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 229 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. #26011388 | C2 | semidirect |
| 4. #26011386 | C2 | semidirect |
| 12. C2×#14583805 | C4 | semidirect |
| 53. C2×Dic173 | C4⋊C4 | semidirect |
| 94. C173 | #2316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149635 | 2 |
| C22×#14583805 | 2 |
| #26011388 | 2 |
| #26011386 | 2 |
| #26011351 | 2 |
| #26011349 | 2 |
| #380×C173 | 2 |
| #2316 | 173 |