Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26011887 | C2 | semidirect |
| 4. #26011834 | C2 | semidirect |
| 5. #26011820 | C2 | semidirect |
| 6. #26011777 | C2 | semidirect |
| 7. #26011748 | C2 | semidirect |
| 8. C4×#14583816 | C2 | semidirect |
| 10. #26011532 | C2 | semidirect |
| 11. #477×C173 | C2 | semidirect |
| 116. C173 | #3356 | semidirect |
| 123. #477 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012214 | 2 |
| #26012202 | 2 |
| #26011887 | 2 |
| #26011834 | 2 |
| #26011820 | 2 |
| #26011777 | 2 |
| #26011748 | 2 |
| C4×#14583816 | 2 |
| #26011568 | 2 |
| #26011532 | 2 |
| #477×C173 | 2 |
| #3356 | 173 |