Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
476 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 253 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. #26011534 | C2 | semidirect |
| 4. #26011531 | C2 | semidirect |
| 5. #26011527 | C2 | semidirect |
| 6. C2×#19149612 | C2 | semidirect |
| 8. #19149686 | C4 | semidirect |
| 26. #14583810 | C2×C4 | semidirect |
| 27. C2×#13063436 | C2×C4 | semidirect |
| 76. C173 | #2913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149686 | 2 |
| #26011974 | 2 |
| #26011534 | 2 |
| #26011531 | 2 |
| #26011527 | 2 |
| C2×#19149612 | 2 |
| #520×C173 | 2 |
| #2913 | 173 |