Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19149709 | C2 | semidirect |
| 2. C22×#14583814 | C2 | semidirect |
| 3. #26011968 | C2 | semidirect |
| 4. #26011710 | C2 | semidirect |
| 5. #26011688 | C2 | semidirect |
| 6. #26011518 | C2 | semidirect |
| 7. #26011496 | C2 | semidirect |
| 8. #26011487 | C2 | semidirect |
| 12. C2×#14583816 | C22 | semidirect |
| 15. C2×#14583814 | C22 | semidirect |
| 18. C4×Dic346 | C22 | semidirect |
| 22. C4⋊#13063436 | C22 | semidirect |
| 23. #19149603 | C22 | semidirect |
| 25. #19149600 | C22 | semidirect |
| 35. C2×Dic346 | D4 | semidirect |
| 116. C173 | #3043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149709 | 2 |
| C22×#14583814 | 2 |
| #26011968 | 2 |
| #26011710 | 2 |
| #26011688 | 2 |
| #26011518 | 2 |
| #26011496 | 2 |
| #26011487 | 2 |
| #535×C173 | 2 |
| #3043 | 173 |