Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #29507673 | C2 | semidirect |
| 5. C2×#21440553 | C2 | semidirect |
| 6. #29507481 | C2 | semidirect |
| 7. #339×C241 | C2 | semidirect |
| 10. #21440650 | C4 | semidirect |
| 16. #21440570 | C4 | semidirect |
| 17. #21440565 | C4 | semidirect |
| 18. #21440562 | C4 | semidirect |
| 98. C241 | #1765 | semidirect |
| 106. #339 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21440650 | 2 |
| C2×#21440570 | 2 |
| #29507711 | 2 |
| #29507673 | 2 |
| C2×#21440553 | 2 |
| #29507481 | 2 |
| #339×C241 | 2 |
| #1765 | 241 |