Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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. #29507733 | C2 | semidirect |
| 3. #29507713 | C2 | semidirect |
| 4. #29507711 | C2 | semidirect |
| 5. #29507690 | C2 | semidirect |
| 6. #29507685 | C2 | semidirect |
| 7. #421×C241 | C2 | semidirect |
| 10. #21440689 | C4 | semidirect |
| 12. #21440688 | C4 | semidirect |
| 20. C22×#14515349 | C22 | semidirect |
| 21. #21440601 | C22 | semidirect |
| 30. C2×M16×C241 | C22 | semidirect |
| 31. #117×C241 | C22 | semidirect |
| 166. C241 | #1794 | semidirect |
| 170. #421 | D241 | semidirect |
| 188. C2×M16 | C2×D241 | semidirect |
| 191. #117 | C2×D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29508553 | 2 |
| #29507733 | 2 |
| #29507713 | 2 |
| #29507711 | 2 |
| #29507690 | 2 |
| #29507685 | 2 |
| #421×C241 | 2 |
| #1794 | 241 |