Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10597433 | C2 | semidirect |
| 2. C2×#10597396 | C2 | semidirect |
| 3. #11927122 | C2 | semidirect |
| 4. #11926705 | C2 | semidirect |
| 5. #11926698 | C2 | semidirect |
| 6. #11926688 | C2 | semidirect |
| 7. #11926681 | C2 | semidirect |
| 8. #11926546 | C2 | semidirect |
| 9. C2×#10597292 | C2 | semidirect |
| 10. #11926512 | C2 | semidirect |
| 11. C2×C19×#137 | C2 | semidirect |
| 49. C2×Q8×C19 | D4 | semidirect |
| 71. #64541 | D4 | semidirect |
| 164. C2×#137 | D19 | semidirect |
| 214. C19 | #3013 | semidirect |
| 233. C2×Q8 | C22⋊D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597433 | 2 |
| C2×#10597396 | 2 |
| #11927122 | 2 |
| #11926705 | 2 |
| #11926698 | 2 |
| #11926688 | 2 |
| #11926681 | 2 |
| #11926546 | 2 |
| C2×#10597292 | 2 |
| #11926512 | 2 |
| C2×C19×#137 | 2 |
| #3013 | 19 |