Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
816 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 3. #29507590 | C2 | semidirect |
| 4. #29507589 | C2 | semidirect |
| 5. #29507575 | C2 | semidirect |
| 9. C2×#16838749 | C22 | semidirect |
| 11. C2×C22⋊Dic241 | C4 | semidirect |
| 16. #21440549 | C22 | semidirect |
| 25. C22×Dic241 | C2×C4 | semidirect |
| 31. C22⋊Dic241 | C2×C4 | semidirect |
| 32. C22⋊Dic241 | C2×C4 | semidirect |
| 57. C23×C241 | C4⋊C4 | semidirect |
| 98. C241 | #2315 | semidirect |
| 150. C23 | #16838749 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic241 | 2 |
| #29507590 | 2 |
| #29507589 | 2 |
| #29507575 | 2 |
| C22×C22⋊C4×C241 | 2 |
| #2315 | 241 |