Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
984 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊D3×C3⋊D9 |
| commutator, Fitting, cosocle | C2×C33×C9 | C22 |
| Frattini | C2×C3 | C3⋊D32 |
| socle | C2×C34 | C2×D3 |
| hypocenter | C33×C9 | D4 |
| LCS | G ▷ C2×C33×C9 ▷ C33×C9 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C9×C3⋊D3 | C2 | semidirect |
| 2. C2×C32×C3⋊D9 | C2 | semidirect |
| 3. C3⋊(C3⋊(C3⋊Dic9)) | C2 | semidirect |
| 13. C2×C9×C3⋊D3 | D3 | semidirect |
| 14. C2×C3×C3⋊D9 | D3 | semidirect |
| 21. C33×C9 | D4 | semidirect |
| 39. C2×C3×C3⋊D3 | D9 | semidirect |
| 50. C2×C3⋊D9 | C3⋊D3 | semidirect |
| 62. C32×C9 | #67 | semidirect |
| 63. C32×C9 | #67 | semidirect |
| 93. C2×C3⋊D3 | C3⋊D9 | semidirect |
| 113. C33 | #611 | semidirect |
| 120. C3×C9 | #625 | semidirect |
| 121. C3×C9 | #638 | semidirect |
| 162. C32 | #6194 | semidirect |
| 163. C32 | #6233 | semidirect |
| 167. C9 | #6290 | semidirect |
| 185. C3 | #10619877 | semidirect |
| 186. C3 | #10619879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×C3⋊D3 | 2 |
| C2×C32×C3⋊D9 | 2 |
| C3⋊(C3⋊(C3⋊Dic9)) | 2 |
| #10620151 | 3 |
| #10619879 | 3 |
| #10619877 | 3 |