Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
162 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 4. C2×#14583810 | C4 | semidirect |
| 5. C22×#13063436 | C4 | semidirect |
| 13. #101×C173 | C4 | semidirect |
| 73. C173 | #1395 | semidirect |
| 83. #101 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011465 | 2 |
| #26011458 | 2 |
| #413×C173 | 2 |
| #1395 | 173 |