Finite Group DatabasebetaFinite Group DatabasebetaOrder 30861.
100 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 44 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. #23779835 | C3 | semidirect |
| 2. #23779834 | C3 | semidirect |
| 3. #23779833 | C3 | semidirect |
| 4. #23779833 | C3 | semidirect |
| 5. #23779833 | C3 | semidirect |
| 6. #23779833 | C3 | semidirect |
| 7. #23779833 | C3 | semidirect |
| 8. #23779833 | C3 | semidirect |
| 12. C9×#11765917 | C3 | semidirect |
| 50. C127 | #6897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23779835 | 3 |
| #23779834 | 3 |
| #23779833 | 3 |
| C32⋊#11765917 | 3 |
| C9×#11765917 | 3 |
| C32⋊C9×C127 | 3 |
| #6897 | 127 |