Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
270 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 4. #26011217 | C2 | semidirect |
| 5. #26011216 | C2 | semidirect |
| 6. #26011216 | C2 | semidirect |
| 7. #324×C173 | C2 | semidirect |
| 119. C173 | #1472 | semidirect |
| 127. #324 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149657 | 2 |
| #26011453 | 2 |
| C22⋊C8×D173 | 2 |
| #26011217 | 2 |
| #26011216 | 2 |
| #324×C173 | 2 |
| #1472 | 173 |