Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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. #29508293 | C2 | semidirect |
| 3. C2×#21440630 | C2 | semidirect |
| 4. C2×#21440570 | C2 | semidirect |
| 5. #29507721 | C2 | semidirect |
| 6. C2×#21440560 | C2 | semidirect |
| 7. #339×C241 | C2 | semidirect |
| 130. C241 | #2003 | semidirect |
| 138. #339 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21440670 | 2 |
| #29508293 | 2 |
| C2×#21440630 | 2 |
| C2×#21440570 | 2 |
| #29507721 | 2 |
| C2×#21440560 | 2 |
| #339×C241 | 2 |
| #2003 | 241 |