Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
178 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 46 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. #23782905 | C3 | semidirect |
| 2. #23782838 | C3 | semidirect |
| 3. #23782766 | C3 | semidirect |
| 4. #23782764 | C3 | semidirect |
| 5. #23782760 | C3 | semidirect |
| 6. #23782758 | C3 | semidirect |
| 7. #23782752 | C3 | semidirect |
| 8. #23782749 | C3 | semidirect |
| 9. C43×#6912 | C3 | semidirect |
| 58. #6912 | C43⋊C3 | semidirect |
| 86. C43 | #10624854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782905 | 3 |
| #23782838 | 3 |
| #23782766 | 3 |
| #23782764 | 3 |
| #23782760 | 3 |
| #23782758 | 3 |
| #23782752 | 3 |
| #23782749 | 3 |
| C43×#6912 | 3 |
| #10624854 | 43 |