Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26011891 | C2 | semidirect |
| 3. #26011869 | C2 | semidirect |
| 4. #26011858 | C2 | semidirect |
| 8. #26011599 | C2 | semidirect |
| 9. C4×#14583816 | C2 | semidirect |
| 11. #441×C173 | C2 | semidirect |
| 103. C173 | #3177 | semidirect |
| 113. #441 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012099 | 2 |
| #26011891 | 2 |
| #26011869 | 2 |
| #26011858 | 2 |
| #26011750 | 2 |
| #26011746 | 2 |
| #26011731 | 2 |
| #26011599 | 2 |
| C4×#14583816 | 2 |
| #26011448 | 2 |
| #441×C173 | 2 |
| #3177 | 173 |