Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1680 conjugacy classes of subgroups; only the 629 normal subgroups are shown.
This group has 1680 conjugacy classes of subgroups — too many to draw. Only its 629 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 |
|---|---|---|
| 2. Q8×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 4. #11722205 | C2 | semidirect |
| 6. #11722188 | C2 | semidirect |
| 7. #11722185 | C2 | semidirect |
| 12. C33×SD16 | C4 | semidirect |
| 30. C33×Q8 | C2×C4 | semidirect |
| 40. C33×C8 | C2×C4 | semidirect |
| 46. C32×SD16 | Dic3 | semidirect |
| 75. C32×Q8 | C2×Dic3 | semidirect |
| 85. C32×C8 | C2×Dic3 | semidirect |
| 95. C3×SD16 | C3⋊Dic3 | semidirect |
| 122. C33 | #440 | semidirect |
| 125. C3×Q8 | C2×C3⋊Dic3 | semidirect |
| 135. C3×C8 | C2×C3⋊Dic3 | semidirect |
| 144. SD16 | C3⋊(C3⋊Dic3) | semidirect |
| 164. C32 | #5164 | semidirect |
| 167. Q8 | C2×C3⋊(C3⋊Dic3) | semidirect |
| 178. C8 | C2×C3⋊(C3⋊Dic3) | semidirect |
| 194. C3 | #10592863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×SD16 | 2 |
| Q8×C3⋊(C3⋊Dic3) | 2 |
| D4×C3⋊(C3⋊Dic3) | 2 |
| #11722205 | 2 |
| #11722202 | 2 |
| #11722188 | 2 |
| #11722185 | 2 |
| #10592863 | 3 |