Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
532 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 84 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 | #11758088 |
| commutator, Fitting, cosocle | C2×C33×C9 | C22 |
| Frattini | C2×C3 | C3⋊#1113 |
| socle, prime radical | C2×C34 | C2×D3 |
| hypocenter | C33×C9 | Q8 |
| 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 |
|---|---|---|
| 20. C33×C9 | Q8 | semidirect |
| 60. C32×C9 | Dic6 | semidirect |
| 61. C32×C9 | Dic6 | semidirect |
| 109. C33 | Dic18 | semidirect |
| 119. C3×C9 | #627 | semidirect |
| 120. C3×C9 | #634 | semidirect |
| 160. C32 | #6189 | semidirect |
| 161. C32 | #6189 | semidirect |
| 167. C9 | #6293 | semidirect |
| 183. C3 | #10619867 | semidirect |
| 184. C3 | #10619895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×C3⋊(C3⋊Dic3) | 2 |
| C3×C3⋊(C3⋊Dic9) | 2 |
| C32×C3⋊Dic9 | 2 |
| C3⋊#6296 | 3 |
| #10619895 | 3 |
| #10619867 | 3 |