Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
524 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 205 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. #29507601 | C2 | semidirect |
| 4. C4×#16838749 | C2 | semidirect |
| 6. #29507563 | C2 | semidirect |
| 7. C43×C241 | C2 | semidirect |
| 9. #21440599 | C4 | semidirect |
| 75. C241 | #2298 | semidirect |
| 83. C43 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21440599 | 2 |
| #29507608 | 2 |
| #29507601 | 2 |
| C4×#16838749 | 2 |
| C4×#16838747 | 2 |
| #29507563 | 2 |
| C43×C241 | 2 |
| #2298 | 241 |