Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
292 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 109 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×#21440571 | C2 | semidirect |
| 5. #29507472 | C2 | semidirect |
| 6. #29507471 | C2 | semidirect |
| 7. C2×C4×C8×C241 | C2 | semidirect |
| 40. #16838747 | C8 | semidirect |
| 122. C241 | #1923 | semidirect |
| 127. C2×C4×C8 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21440571 | 2 |
| C2×#21440554 | 2 |
| C4×#16838747 | 2 |
| #29507472 | 2 |
| #29507471 | 2 |
| C2×C4×C8×C241 | 2 |
| #1923 | 241 |