Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
552 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 552 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. C4×Dic346 | C4 | semidirect |
| 48. Dic346 | C4⋊C4 | semidirect |
| 89. C173 | #2351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic346 | 2 |
| #26011389 | 2 |
| #26011386 | 2 |
| #26011357 | 2 |
| #26011355 | 2 |
| #26011342 | 2 |
| C4×C4⋊C4×C173 | 2 |
| #2351 | 173 |