Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. C2×#21440648 | C2 | semidirect |
| 3. C2×#21440570 | C2 | semidirect |
| 4. C2×#21440570 | C2 | semidirect |
| 5. #29507683 | C2 | semidirect |
| 6. #29507482 | C2 | semidirect |
| 7. #336×C241 | C2 | semidirect |
| 12. C2×Dic964 | C4 | semidirect |
| 13. C2×#16838759 | C4 | semidirect |
| 14. C2×#16838759 | C4 | semidirect |
| 15. C2×D1928 | C4 | semidirect |
| 130. C241 | #1876 | semidirect |
| 138. #336 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21440664 | 2 |
| C2×#21440648 | 2 |
| C2×#21440570 | 2 |
| #29507683 | 2 |
| #29507482 | 2 |
| #336×C241 | 2 |
| #1876 | 241 |