Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
226 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 52 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. #23782877 | C3 | semidirect |
| 2. C3×C9×C43⋊C9 | C3 | semidirect |
| 3. #23782753 | C3 | semidirect |
| 4. #23782752 | C3 | semidirect |
| 5. #23782750 | C3 | semidirect |
| 6. #23782749 | C3 | semidirect |
| 7. #23782748 | C3 | semidirect |
| 8. #23782745 | C3 | semidirect |
| 9. C43×#6908 | C3 | semidirect |
| 65. #6908 | C43⋊C3 | semidirect |
| 96. C43 | #10624837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782877 | 3 |
| C3×C9×C43⋊C9 | 3 |
| #23782753 | 3 |
| #23782752 | 3 |
| #23782750 | 3 |
| #23782749 | 3 |
| #23782748 | 3 |
| #23782745 | 3 |
| C43×#6908 | 3 |
| #10624837 | 43 |