Finite Group DatabasebetaFinite Group DatabasebetaOrder 2016.
238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 2. C3×#66627 | C2 | semidirect |
| 10. #66627 | D3 | semidirect |
| 51. C32×C7 | #100 | semidirect |
| 88. C3×C7 | #823 | semidirect |
| 108. C32 | #6407 | semidirect |
| 113. C7 | #63559 | semidirect |
| 127. C3 | #10620494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×C4⋊(C3⋊D3) | 2 |
| C3×#66627 | 2 |
| #10620494 | 3 |
| #63559 | 7 |