Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
716 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 114 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×C32 | D3×D9 |
| commutator, cosocle | C2×C3×C9 | C22×C32 |
| Frattini | C2×C3 | C32×D32 |
| Fitting | C2×C33×C9 | C22 |
| socle | C2×C34 | C2×D3 |
| hypocenter | C3×C9 | C32×D4 |
| LCS | G ▷ C2×C3×C9 ▷ C3×C9 | |
| UCS | C1 ◁ C2×C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C32×D3×C9 | C2 | semidirect |
| 2. C2×C33×D9 | C2 | semidirect |
| 3. C32×C3⋊Dic9 | C2 | semidirect |
| 6. C3×#6194 | C3 | direct (N × H) |
| 15. C2×C3×D3×C9 | C2×C3 | semidirect |
| 17. C2×C32×D9 | D3 | semidirect |
| 18. C2×C32×D9 | C2×C3 | semidirect |
| 19. C3×C3⋊Dic9 | C2×C3 | semidirect |
| 22. C33×C9 | D4 | semidirect |
| 27. #6194 | C32 | direct (N × H) |
| 49. C2×C32×D3 | D9 | semidirect |
| 58. C2×D3×C9 | C2×C32 | semidirect |
| 60. C2×C3×D9 | C3×D3 | semidirect |
| 61. C2×C3×D9 | C2×C32 | semidirect |
| 62. C3⋊Dic9 | C2×C32 | semidirect |
| 70. C32×C9 | #67 | semidirect |
| 71. C32×C9 | C3×D4 | semidirect |
| 118. C2×C3×D3 | C3×D9 | semidirect |
| 127. C2×D9 | C32×D3 | semidirect |
| 134. C33 | #611 | semidirect |
| 144. C3×C9 | C3×#67 | semidirect |
| 145. C3×C9 | C32×D4 | semidirect |
| 187. C2×D3 | C32×D9 | semidirect |
| 200. C32 | #6194 | direct (N × H) |
| 201. C32 | C3×#611 | semidirect |
| 207. C9 | C32×#67 | semidirect |
| 231. C3 | C3×#6194 | direct (N × H) |
| 232. C3 | C32×#611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D3×C9 | 2 |
| C2×C33×D9 | 2 |
| C32×C3⋊Dic9 | 2 |
| C32×#625 | 3 |
| C32×#611 | 3 |
| C3×#6194 | 3 |