Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
200 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 43 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. #23782901 | C3 | semidirect |
| 2. #23782889 | C3 | semidirect |
| 3. #23782846 | C3 | semidirect |
| 4. #23782769 | C3 | semidirect |
| 5. #23782756 | C3 | semidirect |
| 6. #23782747 | C3 | semidirect |
| 7. C43×#6879 | C3 | semidirect |
| 12. #16812515 | C32 | semidirect |
| 18. #16812499 | C32 | semidirect |
| 20. C43×#732 | C32 | semidirect |
| 21. C92×C43 | C32 | semidirect |
| 55. #6879 | C43⋊C3 | semidirect |
| 71. #732 | C3×C43⋊C3 | semidirect |
| 76. C92 | C3×C43⋊C3 | semidirect |
| 77. C43 | #10624851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782901 | 3 |
| #23782889 | 3 |
| #23782846 | 3 |
| #23782769 | 3 |
| #23782756 | 3 |
| #23782747 | 3 |
| C43×#6879 | 3 |
| #10624851 | 43 |