Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2212 conjugacy classes of subgroups; only the 795 normal subgroups are shown.
This group has 2212 conjugacy classes of subgroups — too many to draw. Only its 795 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. #11723967 | C2 | semidirect |
| 3. #11722204 | C2 | semidirect |
| 7. C2×C33×Q8 | C4 | semidirect |
| 8. C2×C33×D4 | C4 | semidirect |
| 10. C22×C33×C4 | C4 | semidirect |
| 34. C2×C32×Q8 | Dic3 | semidirect |
| 35. C2×C32×D4 | Dic3 | semidirect |
| 37. C22×C32×C4 | Dic3 | semidirect |
| 75. C2×C3×Q8 | C3⋊Dic3 | semidirect |
| 76. C2×C3×D4 | C3⋊Dic3 | semidirect |
| 78. C22×C3×C4 | C3⋊Dic3 | semidirect |
| 96. C33 | #410 | semidirect |
| 116. C2×Q8 | C3⋊(C3⋊Dic3) | semidirect |
| 117. C2×D4 | C3⋊(C3⋊Dic3) | semidirect |
| 119. C22×C4 | C3⋊(C3⋊Dic3) | semidirect |
| 134. C32 | #5240 | semidirect |
| 162. C3 | #10592939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×#41 | 2 |
| #11723967 | 2 |
| #11722204 | 2 |
| #10592939 | 3 |