Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
524 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 3. #26011375 | C2 | semidirect |
| 4. C4×#14583805 | C2 | semidirect |
| 6. #26011337 | C2 | semidirect |
| 7. C43×C173 | C2 | semidirect |
| 9. #19149636 | C4 | semidirect |
| 75. C173 | #2298 | semidirect |
| 83. C43 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149636 | 2 |
| #26011382 | 2 |
| #26011375 | 2 |
| C4×#14583805 | 2 |
| C4×#14583803 | 2 |
| #26011337 | 2 |
| C43×C173 | 2 |
| #2298 | 173 |