Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
374 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 46 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 | #11757748 |
| commutator, Fitting, cosocle | C2×C9×H(3,𝔽3) | C22 |
| Frattini, socle | C2×C32 | #1113 |
| hypocenter | C9×H(3,𝔽3) | D4 |
| LCS | G ▷ C2×C9×H(3,𝔽3) ▷ C9×H(3,𝔽3) | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C9×#272 | C2 | semidirect |
| 2. C2×#92297 | C2 | semidirect |
| 3. #11757601 | C2 | semidirect |
| 10. C2×C3⋊(C3⋊D9) | D3 | semidirect |
| 17. C3⋊(C3⋊Dic9) | D3 | semidirect |
| 22. C9×H(3,𝔽3) | D4 | semidirect |
| 52. C2×#272 | D9 | semidirect |
| 70. C32×C9 | D12 | semidirect |
| 71. C32×C9 | #67 | semidirect |
| 150. H(3,𝔽3) | #611 | semidirect |
| 229. C32 | #6194 | semidirect |
| 230. C32 | #6195 | semidirect |
| 235. C9 | #6200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#272 | 2 |
| C2×#92297 | 2 |
| #11757601 | 2 |
| #10619904 | 3 |
| #10619880 | 3 |
| #10619879 | 3 |