Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. C2×#19149701 | C2 | semidirect |
| 2. #26012162 | C2 | semidirect |
| 3. #26011868 | C2 | semidirect |
| 4. #26011727 | C2 | semidirect |
| 5. #26011692 | C2 | semidirect |
| 6. #26011638 | C2 | semidirect |
| 7. C4×Dic692 | C2 | semidirect |
| 8. C8×D4×C173 | C2 | semidirect |
| 38. Dic692 | D4 | semidirect |
| 87. C4×C173 | #135 | semidirect |
| 97. C173 | #3287 | semidirect |
| 106. C8×D4 | D173 | semidirect |
| 187. C4 | #19149701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149701 | 2 |
| #26012162 | 2 |
| #26011868 | 2 |
| #26011727 | 2 |
| #26011692 | 2 |
| #26011638 | 2 |
| C4×Dic692 | 2 |
| C8×D4×C173 | 2 |
| #3287 | 173 |