Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
338 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. #26011893 | C2 | semidirect |
| 3. #26011859 | C2 | semidirect |
| 6. #26011598 | C2 | semidirect |
| 7. Q16×Dic173 | C2 | semidirect |
| 9. #494×C173 | C2 | semidirect |
| 78. C173 | #3177 | semidirect |
| 82. #494 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012102 | 2 |
| #26011893 | 2 |
| #26011859 | 2 |
| #26011746 | 2 |
| #26011729 | 2 |
| #26011598 | 2 |
| Q16×Dic173 | 2 |
| #26011445 | 2 |
| #494×C173 | 2 |
| #3177 | 173 |