Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
438 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 69 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×C9 | #1113 |
| commutator | C2×C33 | C22×C9 |
| Frattini | C2×C3 | C3×#1113 |
| Fitting | C2×C33×C9 | C22 |
| socle, prime radical, cosocle | C2×C34 | C22×C3 |
| hypocenter | C33 | Q8×C9 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2×C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. C33×C9 | Q8 | semidirect |
| 11. #6296 | C9 | direct (N × H) |
| 37. C32×C9 | Dic6 | semidirect |
| 73. C33 | Q8×C9 | semidirect |
| 84. C3×C9 | #627 | semidirect |
| 120. C32 | C9×Dic6 | semidirect |
| 125. C9 | #6296 | direct (N × H) |
| 140. C3 | C9×#627 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×C3⋊Dic3 | 2 |
| C3×#6296 | 3 |
| C9×#627 | 3 |