Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
166 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 166 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 |
|---|---|---|
| 1. #26011887 | C2 | semidirect |
| 5. #26011241 | C2 | semidirect |
| 6. #26011239 | C2 | semidirect |
| 7. #332×C173 | C2 | semidirect |
| 51. #13063436 | SD16 | semidirect |
| 76. C173 | #1671 | semidirect |
| 84. #332 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011887 | 2 |
| #26011782 | 2 |
| #26011693 | 2 |
| #26011556 | 2 |
| #26011241 | 2 |
| #26011239 | 2 |
| #332×C173 | 2 |
| #1671 | 173 |