Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
588 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 588 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. #29507734 | C2 | semidirect |
| 3. #29507723 | C2 | semidirect |
| 4. #29507721 | C2 | semidirect |
| 5. #29507699 | C2 | semidirect |
| 6. #29507690 | C2 | semidirect |
| 7. #421×C241 | C2 | semidirect |
| 12. C2×#16838771 | C4 | semidirect |
| 18. C2×D4×D241 | C4 | semidirect |
| 19. C2×#16838754 | C22 | semidirect |
| 20. #21440601 | C22 | semidirect |
| 28. C2×M16×C241 | C22 | semidirect |
| 29. #117×C241 | C22 | semidirect |
| 153. C241 | #1795 | semidirect |
| 157. #421 | D241 | semidirect |
| 175. C2×M16 | C2×D241 | semidirect |
| 177. #117 | C2×D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21440688 | 2 |
| #29507734 | 2 |
| #29507723 | 2 |
| #29507721 | 2 |
| #29507699 | 2 |
| #29507690 | 2 |
| #421×C241 | 2 |
| #1795 | 241 |