Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
214 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 52 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 | D92 |
| commutator, cosocle | C2×C92 | C22×C3 |
| Frattini | C2×C32 | C3×D32 |
| Fitting | C2×C3×C92 | C22 |
| socle, prime radical | C2×C33 | D32 |
| hypocenter | C92 | C3×Q8 |
| LCS | G ▷ C2×C92 ▷ C92 | |
| UCS | C1 ◁ C2×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10619531 | C3 | direct (N × H) |
| 13. C3×C92 | Q8 | semidirect |
| 39. C92 | C3×Q8 | semidirect |
| 76. C3×C9 | Dic18 | semidirect |
| 108. C9 | C3×Dic18 | semidirect |
| 120. C3 | #10619531 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9⋊Dic9 | 2 |
| C3×C9×Dic9 | 2 |
| C3×#6189 | 3 |
| #10619531 | 3 |