Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
218 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 28. C33×C8 | Q8 | semidirect |
| 29. C3×C3⋊(C3⋊C8) | Q8 | semidirect |
| 63. C32×C8 | Dic6 | semidirect |
| 64. C3⋊(C3⋊C8) | Dic6 | semidirect |
| 95. C33 | #446 | semidirect |
| 107. C3×C8 | PSU(3,𝔽2) | semidirect |
| 138. C32 | #4679 | semidirect |
| 148. C8 | C3⋊PSU(3,𝔽2) | semidirect |
| 165. C3 | #10593532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C3⋊PSU(3,𝔽2) | 2 |
| #11723092 | 2 |
| C3×C8×#157 | 2 |
| #11722804 | 2 |
| #11722803 | 2 |
| #10593532 | 3 |
| #4679 | 9 |