Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
692 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 692 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 | C2×C34 | C2×D3 |
| hypocenter | C33×C9 | D4 |
| 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 |
|---|---|---|
| 1. C2×C3×C3⋊(C3⋊D9) | C2 | semidirect |
| 2. C2×C32×C3⋊D9 | C2 | semidirect |
| 3. C9×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 13. C2×C3⋊(C3⋊D9) | D3 | semidirect |
| 16. C2×C3×C3⋊D9 | D3 | semidirect |
| 22. C33×C9 | D4 | semidirect |
| 51. C3⋊(C3⋊Dic3) | D9 | semidirect |
| 57. C2×C3⋊D9 | C3⋊D3 | semidirect |
| 70. C32×C9 | #67 | semidirect |
| 71. C32×C9 | #67 | semidirect |
| 134. C33 | D36 | semidirect |
| 144. C3×C9 | #625 | semidirect |
| 145. C3×C9 | #638 | semidirect |
| 200. C32 | #6192 | semidirect |
| 201. C32 | #6192 | semidirect |
| 207. C9 | #6290 | semidirect |
| 231. C3 | #10619873 | semidirect |
| 232. C3 | #10619897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C3⋊(C3⋊D9) | 2 |
| C2×C32×C3⋊D9 | 2 |
| C9×C3⋊(C3⋊Dic3) | 2 |
| #10620157 | 3 |
| #10619897 | 3 |
| #10619873 | 3 |