Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 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. #41×Dic241 | C2 | semidirect |
| 3. C2×#21440568 | C2 | semidirect |
| 4. #29507690 | C2 | semidirect |
| 5. #29507488 | C2 | semidirect |
| 6. #29507476 | C2 | semidirect |
| 7. #421×C241 | C2 | semidirect |
| 10. #21440672 | C4 | semidirect |
| 12. #21440667 | C4 | semidirect |
| 33. C2×Dic482 | C2×C4 | semidirect |
| 34. C2×D964 | C2×C4 | semidirect |
| 44. #16838754 | C2×C4 | semidirect |
| 129. C241 | #1906 | semidirect |
| 133. #421 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29508515 | 2 |
| #41×Dic241 | 2 |
| C2×#21440568 | 2 |
| #29507690 | 2 |
| #29507488 | 2 |
| #29507476 | 2 |
| #421×C241 | 2 |
| #1906 | 241 |