Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
500 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 73 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. C32×#11923958 | C3 | semidirect |
| 2. C3×#16812510 | C3 | semidirect |
| 3. #23782798 | C3 | semidirect |
| 5. C3×C43×C32⋊C9 | C3 | semidirect |
| 25. #11923958 | H(3,𝔽3) | semidirect |
| 50. C32×C43 | #731 | semidirect |
| 63. C3×C32⋊C9 | C43⋊C3 | semidirect |
| 86. C43 | #10624745 | semidirect |
| 118. C32 | #16812510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11923958 | 3 |
| C3×#16812510 | 3 |
| #23782798 | 3 |
| #23782794 | 3 |
| C3×C43×C32⋊C9 | 3 |
| #10624745 | 43 |