Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19149711 | C2 | semidirect |
| 2. Q8×D692 | C2 | semidirect |
| 4. #26011870 | C2 | semidirect |
| 5. #26011748 | C2 | semidirect |
| 6. #26011697 | C2 | semidirect |
| 7. #26011656 | C2 | semidirect |
| 8. #26011645 | C2 | semidirect |
| 9. C4×#14583813 | C2 | semidirect |
| 10. #26011568 | C2 | semidirect |
| 11. #462×C173 | C2 | semidirect |
| 58. #14583813 | D4 | semidirect |
| 123. C4×C173 | #137 | semidirect |
| 134. C173 | #3276 | semidirect |
| 141. #462 | D173 | semidirect |
| 261. C4 | #19149711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149711 | 2 |
| Q8×D692 | 2 |
| #26012144 | 2 |
| #26011870 | 2 |
| #26011748 | 2 |
| #26011697 | 2 |
| #26011656 | 2 |
| #26011645 | 2 |
| C4×#14583813 | 2 |
| #26011568 | 2 |
| #462×C173 | 2 |
| #3276 | 173 |