Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
370 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26012219 | C2 | semidirect |
| 3. #26011843 | C2 | semidirect |
| 4. #26011840 | C2 | semidirect |
| 5. #26011775 | C2 | semidirect |
| 8. #26011615 | C2 | semidirect |
| 11. #475×C173 | C2 | semidirect |
| 78. Dic346 | SD16 | semidirect |
| 118. C173 | #3359 | semidirect |
| 125. #475 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012219 | 2 |
| #26012156 | 2 |
| #26011843 | 2 |
| #26011840 | 2 |
| #26011775 | 2 |
| #26011697 | 2 |
| #26011695 | 2 |
| #26011615 | 2 |
| C4×#14583813 | 2 |
| #26011578 | 2 |
| #475×C173 | 2 |
| #3359 | 173 |