Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
342 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 2. #26011887 | C2 | semidirect |
| 3. #26011832 | C2 | semidirect |
| 4. #26011819 | C2 | semidirect |
| 5. #26011786 | C2 | semidirect |
| 6. #26011773 | C2 | semidirect |
| 7. #26011747 | C2 | semidirect |
| 8. C4×#14583816 | C2 | semidirect |
| 10. #26011534 | C2 | semidirect |
| 116. C173 | #3356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012198 | 2 |
| #26011887 | 2 |
| #26011832 | 2 |
| #26011819 | 2 |
| #26011786 | 2 |
| #26011773 | 2 |
| #26011747 | 2 |
| C4×#14583816 | 2 |
| #26011569 | 2 |
| #26011534 | 2 |
| #556×C173 | 2 |
| #3356 | 173 |