Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
558 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 64 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 | #66431 |
| commutator, cosocle | C2×C32×C9 | C22×C3 |
| Frattini | C2×C3 | C3×#1113 |
| Fitting | C2×C33×C9 | C22 |
| socle | C2×C34 | C2×D3 |
| hypocenter | C32×C9 | C3×D4 |
| LCS | G ▷ C2×C32×C9 ▷ C32×C9 | |
| UCS | C1 ◁ C2×C3 | |
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. C32×C3⋊Dic9 | C2 | semidirect |
| 5. #10619899 | C3 | direct (N × H) |
| 15. C2×C9×C3⋊D3 | C2×C3 | semidirect |
| 17. C2×C3×C3⋊D9 | D3 | semidirect |
| 18. C2×C3×C3⋊D9 | C2×C3 | semidirect |
| 25. C3×C3⋊Dic9 | D3 | semidirect |
| 26. C3×C3⋊Dic9 | C2×C3 | semidirect |
| 29. C33×C9 | D4 | semidirect |
| 68. C2×C3×C3⋊D3 | D9 | semidirect |
| 83. C2×C3⋊D9 | C3×D3 | semidirect |
| 96. C3⋊Dic9 | C3×D3 | semidirect |
| 115. C32×C9 | D12 | semidirect |
| 116. C32×C9 | #67 | semidirect |
| 117. C32×C9 | C3×D4 | semidirect |
| 198. C2×C3⋊D3 | C3×D9 | semidirect |
| 245. C33 | #611 | semidirect |
| 275. C3×C9 | #626 | semidirect |
| 276. C3×C9 | C3×D12 | semidirect |
| 277. C3×C9 | C3×#67 | semidirect |
| 400. C32 | #6194 | semidirect |
| 401. C32 | #6195 | semidirect |
| 402. C32 | C3×#611 | semidirect |
| 413. C9 | C3×#626 | semidirect |
| 456. C3 | C3×#6194 | semidirect |
| 457. C3 | C3×#6195 | semidirect |
| 458. C3 | #10619899 | direct (N × H) |
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 |
| C32×C3⋊Dic9 | 2 |
| C3×#6295 | 3 |
| #10619899 | 3 |
| C3×#6195 | 3 |
| C3×#6194 | 3 |