Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
334 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 74 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 | D3×C3⋊D27 |
| commutator, Fitting, cosocle | C2×C32×C27 | C22 |
| Frattini | C2×C9 | D3×C3⋊D3 |
| socle | C2×C33 | C2×D9 |
| hypocenter | C32×C27 | D4 |
| LCS | G ▷ C2×C32×C27 ▷ C32×C27 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3⋊(C3⋊D27) | C2 | semidirect |
| 2. C2×C3×D3×C27 | C2 | semidirect |
| 3. C3×C3⋊Dic27 | C2 | semidirect |
| 18. C2×D3×C27 | D3 | semidirect |
| 19. C3⋊Dic27 | D3 | semidirect |
| 21. C32×C27 | D4 | semidirect |
| 62. C3×C27 | D12 | semidirect |
| 63. C3×C27 | #67 | semidirect |
| 98. C2×C3×D3 | D27 | semidirect |
| 119. C27 | #626 | semidirect |
| 153. C2×D3 | C3⋊D27 | semidirect |
| 159. C32 | #6171 | semidirect |
| 185. C3 | #10619545 | semidirect |
| 186. C3 | #10619677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊(C3⋊D27) | 2 |
| C2×C3×D3×C27 | 2 |
| C3×C3⋊Dic27 | 2 |
| #10619880 | 3 |
| #10619677 | 3 |
| #10619545 | 3 |