Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
224 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 91 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. #23782857 | C3 | semidirect |
| 2. C32×C43⋊C27 | C3 | semidirect |
| 3. #23782730 | C3 | semidirect |
| 4. #23782727 | C3 | semidirect |
| 5. #23782718 | C3 | semidirect |
| 70. C43 | #10624724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782857 | 3 |
| C32×C43⋊C27 | 3 |
| #23782730 | 3 |
| #23782727 | 3 |
| #23782718 | 3 |
| C43×#6908 | 3 |
| #10624724 | 43 |