Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26011508 | C2 | semidirect |
| 3. C2×#19149607 | C2 | semidirect |
| 4. #26011464 | C2 | semidirect |
| 5. #26011261 | C2 | semidirect |
| 6. #26011251 | C2 | semidirect |
| 7. C4×#41×C173 | C2 | semidirect |
| 10. #19149709 | C4 | semidirect |
| 12. #19149704 | C4 | semidirect |
| 33. C2×Dic346 | C2×C4 | semidirect |
| 34. C2×D692 | C2×C4 | semidirect |
| 44. #14583810 | C2×C4 | semidirect |
| 129. C173 | #1906 | semidirect |
| 132. C4×#41 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012289 | 2 |
| #26011508 | 2 |
| C2×#19149607 | 2 |
| #26011464 | 2 |
| #26011261 | 2 |
| #26011251 | 2 |
| C4×#41×C173 | 2 |
| #1906 | 173 |