Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 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. #26011899 | C2 | semidirect |
| 3. #26011897 | C2 | semidirect |
| 4. #26011895 | C2 | semidirect |
| 5. #26011893 | C2 | semidirect |
| 6. #26011892 | C2 | semidirect |
| 11. #500×C173 | C2 | semidirect |
| 42. #14583809 | Q8 | semidirect |
| 45. C8×D173 | Q8 | semidirect |
| 107. C173 | #3164 | semidirect |
| 113. #500 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012118 | 2 |
| #26011899 | 2 |
| #26011897 | 2 |
| #26011895 | 2 |
| #26011893 | 2 |
| #26011892 | 2 |
| #26011532 | 2 |
| #26011528 | 2 |
| #107×D173 | 2 |
| #26011445 | 2 |
| #500×C173 | 2 |
| #3164 | 173 |