Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 1. C2×#21440675 | C2 | semidirect |
| 2. C2×#21440672 | C2 | semidirect |
| 4. C2×#21440570 | C2 | semidirect |
| 5. #29507623 | C2 | semidirect |
| 6. #29507485 | C2 | semidirect |
| 7. C2×#104×C241 | C2 | semidirect |
| 41. C2×Dic482 | D4 | semidirect |
| 53. #16838754 | D4 | semidirect |
| 71. M16×C241 | D4 | semidirect |
| 144. C241 | #2007 | semidirect |
| 150. C2×#104 | D241 | semidirect |
| 210. M16 | C22⋊D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21440675 | 2 |
| C2×#21440672 | 2 |
| #29508295 | 2 |
| C2×#21440570 | 2 |
| #29507623 | 2 |
| #29507485 | 2 |
| C2×#104×C241 | 2 |
| #2007 | 241 |