Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
540 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 189 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. #26011387 | C2 | semidirect |
| 4. #26011382 | C2 | semidirect |
| 5. #26011353 | C2 | semidirect |
| 6. #26011350 | C2 | semidirect |
| 7. #26011337 | C2 | semidirect |
| 8. C4×C4⋊C4×C173 | C2 | semidirect |
| 11. C4×D692 | C4 | semidirect |
| 96. C173 | #2319 | semidirect |
| 104. C4×C4⋊C4 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D692 | 2 |
| #26011392 | 2 |
| #26011387 | 2 |
| #26011382 | 2 |
| #26011353 | 2 |
| #26011350 | 2 |
| #26011337 | 2 |
| C4×C4⋊C4×C173 | 2 |
| #2319 | 173 |