Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
348 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×#21440675 | C2 | semidirect |
| 3. #29508293 | C2 | semidirect |
| 4. #29507733 | C2 | semidirect |
| 5. #29507727 | C2 | semidirect |
| 6. #29507690 | C2 | semidirect |
| 7. #344×C241 | C2 | semidirect |
| 136. C241 | #2009 | semidirect |
| 144. #344 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29508517 | 2 |
| C2×#21440675 | 2 |
| #29508293 | 2 |
| #29507733 | 2 |
| #29507727 | 2 |
| #29507690 | 2 |
| #344×C241 | 2 |
| #2009 | 241 |