Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
392 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26011861 | C2 | semidirect |
| 3. #26011857 | C2 | semidirect |
| 4. #26011853 | C2 | semidirect |
| 5. #26011485 | C2 | semidirect |
| 6. C2×#19149590 | C2 | semidirect |
| 7. #533×C173 | C2 | semidirect |
| 78. C173 | #3135 | semidirect |
| 80. #533 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012041 | 2 |
| #26011861 | 2 |
| #26011857 | 2 |
| #26011853 | 2 |
| #26011485 | 2 |
| C2×#19149590 | 2 |
| #533×C173 | 2 |
| #3135 | 173 |