Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1179 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 1179 conjugacy classes of subgroups — too many to draw. Only its 288 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C33×Dic6 | C3 | semidirect |
| 5. Dic6×H(3,𝔽3) | C3 | direct (N × H) |
| 15. C32×H(3,𝔽3) | Q8 | semidirect |
| 19. C32×Dic6 | C32 | semidirect |
| 40. C34 | C3×Q8 | semidirect |
| 43. C3×H(3,𝔽3) | Dic6 | direct (N × H) |
| 44. C3×H(3,𝔽3) | C3×Q8 | semidirect |
| 49. C3×Dic6 | H(3,𝔽3) | direct (N × H) |
| 82. C33 | C3×Dic6 | semidirect |
| 84. C33 | C32×Q8 | semidirect |
| 86. H(3,𝔽3) | C3×Dic6 | direct (N × H) |
| 90. Dic6 | C3×H(3,𝔽3) | direct (N × H) |
| 122. C32 | Q8×H(3,𝔽3) | semidirect |
| 124. C32 | C32×Dic6 | semidirect |
| 140. C3 | Dic6×H(3,𝔽3) | direct (N × H) |
| 141. C3 | C3×Q8×H(3,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×H(3,𝔽3) | 2 |
| C3×Dic3×H(3,𝔽3) | 2 |
| C33×Dic6 | 3 |
| C3×Q8×H(3,𝔽3) | 3 |
| Dic6×H(3,𝔽3) | 3 |