Finite Group DatabasebetaFinite Group DatabasebetaOrder 3024.
244 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 49 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×Dic42⋊C3 | C2 | semidirect |
| 3. C3×C3⋊(ΓL(1,𝔽8)⋊C8) | C2 | semidirect |
| 4. #11759220 | C3 | semidirect |
| 11. C3×Dic42 | C2×C3 | semidirect |
| 13. Dic42⋊C3 | D3 | semidirect |
| 18. C3×C3⋊(C7⋊C8) | C2×C3 | semidirect |
| 20. C3⋊(ΓL(1,𝔽8)⋊C8) | D3 | semidirect |
| 46. C32×ΓL(1,𝔽8) | SD16 | semidirect |
| 47. Dic42 | C3×D3 | semidirect |
| 55. C3⋊(C7⋊C8) | C3×D3 | semidirect |
| 104. C32×C7 | C3×SD16 | semidirect |
| 109. C3×ΓL(1,𝔽8) | #204 | semidirect |
| 110. C3×ΓL(1,𝔽8) | #215 | semidirect |
| 162. C3×C7 | C3×#204 | semidirect |
| 163. C3×C7 | C3×#215 | semidirect |
| 167. ΓL(1,𝔽8) | #3717 | semidirect |
| 203. C32 | #1142⋊C3 | semidirect |
| 207. C7 | C3×#3717 | semidirect |
| 227. C3 | #66564⋊C3 | semidirect |
| 228. C3 | #66567⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×C4⋊(C3⋊D3) | 2 |
| C3×Dic42⋊C3 | 2 |
| C3×C3⋊(ΓL(1,𝔽8)⋊C8) | 2 |
| #11759220 | 3 |
| #66567⋊C3 | 3 |
| #66564⋊C3 | 3 |
| C3×#3717 | 7 |