Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
420 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 420 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. C33×Q8 | C8 | semidirect |
| 19. C3⋊#622 | Q8 | direct (N × H) |
| 41. C32×Q8 | C3⋊C8 | semidirect |
| 79. C33 | C8×Q8 | semidirect |
| 82. C3×Q8 | #622 | semidirect |
| 120. C32 | Q8×C3⋊C8 | semidirect |
| 121. Q8 | C3⋊#622 | direct (N × H) |
| 143. C3 | Q8×#622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×C3⋊Dic3 | 2 |
| C4⋊(C3⋊#622) | 2 |
| C4×C3⋊#622 | 2 |
| Q8×#622 | 3 |
| Q8×C3⋊C8 | 9 |