Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1344 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 1344 conjugacy classes of subgroups — too many to draw. Only its 407 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×Q8 | Q8 | semidirect |
| 68. C32×Q8 | Dic6 | semidirect |
| 110. C33 | #475 | semidirect |
| 112. C3×Q8 | #634 | semidirect |
| 146. C32 | #4791 | semidirect |
| 149. Q8 | #6308 | semidirect |
| 171. C3 | #10592490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊(C3⋊Dic3) | 2 |
| #11723929 | 2 |
| C33×#103 | 2 |
| #11722205 | 2 |
| #11722187 | 2 |
| #11722184 | 2 |
| #11722178 | 2 |
| #10592490 | 3 |