Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
150 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26011244 | C2 | semidirect |
| 5. #26011241 | C2 | semidirect |
| 6. #26011241 | C2 | semidirect |
| 7. #335×C173 | C2 | semidirect |
| 74. C173 | #1572 | semidirect |
| 80. #335 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011547 | 2 |
| #26011543 | 2 |
| #26011542 | 2 |
| #26011244 | 2 |
| #26011241 | 2 |
| #335×C173 | 2 |
| #1572 | 173 |