Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C8 | #1113 |
| commutator | C2×C33 | C4×C8 |
| Fitting, cosocle | C2×C33×C8 | C22 |
| socle, prime radical | C22×C33 | C2×C8 |
| hypocenter | C33 | #346 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C3×C3⋊(C3⋊C16) | C4 | semidirect |
| 33. C3⋊(C3⋊C16) | Dic3 | semidirect |
| 104. C33 | #346 | semidirect |
| 158. C32 | #4461 | semidirect |
| 159. C32 | #4502 | semidirect |
| 181. C3 | #10589103 | semidirect |
| 182. C3 | #10589104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×C3⋊Dic3 | 2 |
| C2×C3×C3⋊(C3⋊C16) | 2 |
| #10589104 | 3 |
| #10589103 | 3 |