Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
718 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 108 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 | D3×C3⋊D9 |
| commutator, cosocle | C2×C32×C9 | C22×C3 |
| Frattini | C2×C3 | C3×D3×C3⋊D3 |
| Fitting | C2×C33×C9 | C22 |
| socle | C2×C34 | C2×D3 |
| hypocenter | C32×C9 | C3×D4 |
| LCS | G ▷ C2×C32×C9 ▷ C32×C9 | |
| UCS | C1 ◁ C2×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C32×C3⋊D9 | C2 | semidirect |
| 2. C2×C32×D3×C9 | C2 | semidirect |
| 3. C3×C3⋊(C3⋊Dic9) | C2 | semidirect |
| 6. #10619879 | C3 | direct (N × H) |
| 16. C2×C3×C3⋊D9 | D3 | semidirect |
| 17. C2×C3×C3⋊D9 | C2×C3 | semidirect |
| 20. C2×C3×D3×C9 | D3 | semidirect |
| 21. C2×C3×D3×C9 | C2×C3 | semidirect |
| 23. C3⋊(C3⋊Dic9) | C2×C3 | semidirect |
| 28. C33×C9 | D4 | semidirect |
| 66. C2×C32×D3 | D9 | semidirect |
| 79. C2×C3⋊D9 | C3×D3 | semidirect |
| 81. C2×D3×C9 | C3×D3 | semidirect |
| 99. C32×C9 | #67 | semidirect |
| 100. C32×C9 | #67 | semidirect |
| 101. C32×C9 | C3×D4 | semidirect |
| 172. C2×C3×D3 | C3×D9 | semidirect |
| 173. C2×C3×D3 | C3⋊D9 | semidirect |
| 197. C33 | #611 | semidirect |
| 214. C3×C9 | #625 | semidirect |
| 215. C3×C9 | C3×#67 | semidirect |
| 216. C3×C9 | C3×#67 | semidirect |
| 279. C2×D3 | C3×C3⋊D9 | semidirect |
| 303. C32 | #6194 | semidirect |
| 304. C32 | C3×#611 | semidirect |
| 305. C32 | #6233 | semidirect |
| 312. C9 | C3×#625 | semidirect |
| 346. C3 | C3×#6194 | semidirect |
| 347. C3 | #10619879 | direct (N × H) |
| 348. C3 | C3×#6233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C3⋊D9 | 2 |
| C2×C32×D3×C9 | 2 |
| C3×C3⋊(C3⋊Dic9) | 2 |
| C3×#6290 | 3 |
| C3×#6233 | 3 |
| #10619879 | 3 |
| C3×#6194 | 3 |