Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
960 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 286 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. C3×#16812525 | C3 | semidirect |
| 2. C3×#16812525 | C3 | semidirect |
| 3. #23782900 | C3 | semidirect |
| 4. #23782899 | C3 | semidirect |
| 5. #23782895 | C3 | semidirect |
| 6. #23782891 | C3 | semidirect |
| 7. #23782888 | C3 | semidirect |
| 8. #23782886 | C3 | semidirect |
| 9. #23782883 | C3 | semidirect |
| 10. #23782881 | C3 | semidirect |
| 11. #23782874 | C3 | semidirect |
| 12. C3×C43×#737 | C3 | semidirect |
| 24. #16812525 | C32 | semidirect |
| 25. #16812525 | C32 | semidirect |
| 26. #16812525 | C32 | semidirect |
| 32. C3×#11923957 | C32 | semidirect |
| 34. C3×#11923956 | C32 | semidirect |
| 38. C3×C9×C43⋊C3 | C32 | semidirect |
| 39. #16812514 | C32 | semidirect |
| 41. #16812511 | C32 | semidirect |
| 42. #16812509 | C32 | semidirect |
| 43. #16812508 | C32 | semidirect |
| 44. #16812506 | C32 | semidirect |
| 48. C43×#737 | C32 | semidirect |
| 49. C43×#737 | C32 | semidirect |
| 50. C43×#737 | C32 | semidirect |
| 137. C3×#737 | C43⋊C3 | semidirect |
| 171. #737 | C3×C43⋊C3 | semidirect |
| 172. #737 | C3×C43⋊C3 | semidirect |
| 173. #737 | C3×C43⋊C3 | semidirect |
| 197. C43 | #10624929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#16812525 | 3 |
| #23782900 | 3 |
| #23782899 | 3 |
| #23782895 | 3 |
| #23782891 | 3 |
| #23782888 | 3 |
| #23782886 | 3 |
| #23782883 | 3 |
| #23782881 | 3 |
| #23782874 | 3 |
| C3×C43×#737 | 3 |
| #10624929 | 43 |