Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
300 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 300 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×#21440577 | C2 | semidirect |
| 3. C2×#21440570 | C2 | semidirect |
| 4. #29507685 | C2 | semidirect |
| 5. #29507684 | C2 | semidirect |
| 6. C2×C4×#14515349 | C2 | semidirect |
| 7. C2×#104×C241 | C2 | semidirect |
| 11. C2×#16838760 | C4 | semidirect |
| 12. C2×#16838758 | C4 | semidirect |
| 13. C2×#16838757 | C4 | semidirect |
| 14. C2×#16838755 | C4 | semidirect |
| 119. C241 | #1974 | semidirect |
| 124. C2×#104 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21440662 | 2 |
| C2×#21440577 | 2 |
| C2×#21440570 | 2 |
| #29507685 | 2 |
| #29507684 | 2 |
| C2×C4×#14515349 | 2 |
| C2×#104×C241 | 2 |
| #1974 | 241 |