Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26011870 | C2 | semidirect |
| 3. #26011839 | C2 | semidirect |
| 4. #26011838 | C2 | semidirect |
| 5. #26011837 | C2 | semidirect |
| 6. C8×#13063436 | C2 | semidirect |
| 7. #486×C173 | C2 | semidirect |
| 74. C173 | #1709 | semidirect |
| 81. #486 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011870 | 2 |
| #26011867 | 2 |
| #26011839 | 2 |
| #26011838 | 2 |
| #26011837 | 2 |
| C8×#13063436 | 2 |
| #486×C173 | 2 |
| #1709 | 173 |