Finite Group DatabasebetaFinite Group DatabasebetaOrder 2016.
326 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 326 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 |
|---|---|---|
| 2. C3×#66627 | C2 | semidirect |
| 3. #11759216 | C2 | semidirect |
| 4. #11759214 | C2 | semidirect |
| 13. C3×C3⋊(C7⋊C8) | C22 | semidirect |
| 16. #66627 | D3 | semidirect |
| 44. C3⋊(C7⋊C8) | C2×D3 | semidirect |
| 53. C7×C3⋊D3 | M16 | semidirect |
| 84. C32×C7 | C2×M16 | semidirect |
| 143. C3×C7 | D3×M16 | semidirect |
| 147. C3⋊D3 | #1136 | semidirect |
| 173. C32 | C2×#1136 | semidirect |
| 182. C7 | #63818 | semidirect |
| 202. C3 | D3×#1136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×C3⋊D3 | 2 |
| C3×#66627 | 2 |
| #11759216 | 2 |
| #11759214 | 2 |
| D3×#1136 | 3 |
| #63818 | 7 |