Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 3. #26011889 | C2 | semidirect |
| 4. #26011830 | C2 | semidirect |
| 5. #26011820 | C2 | semidirect |
| 6. #26011786 | C2 | semidirect |
| 7. #26011776 | C2 | semidirect |
| 8. #26011746 | C2 | semidirect |
| 10. #26011532 | C2 | semidirect |
| 11. C4×Q16×C173 | C2 | semidirect |
| 116. C173 | #3356 | semidirect |
| 126. C4×Q16 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012214 | 2 |
| #26012201 | 2 |
| #26011889 | 2 |
| #26011830 | 2 |
| #26011820 | 2 |
| #26011786 | 2 |
| #26011776 | 2 |
| #26011746 | 2 |
| #26011570 | 2 |
| #26011532 | 2 |
| C4×Q16×C173 | 2 |
| #3356 | 173 |