Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
11116 conjugacy classes of subgroups; only the 2267 normal subgroups are shown.
This group has 11116 conjugacy classes of subgroups — too many to draw. Only its 2267 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 |
|---|---|---|
| 1. C22×C33×Q8 | C2 | semidirect |
| 2. #11724682 | C2 | direct (N × H) |
| 3. C2×#89080 | C2 | semidirect |
| 4. C2×Q8×C3⋊(C3⋊D3) | C2 | semidirect |
| 5. C2×#89076 | C2 | semidirect |
| 8. C2×C33×Q8 | C22 | semidirect |
| 11. #89080 | C22 | semidirect |
| 12. Q8×C3⋊(C3⋊D3) | C22 | semidirect |
| 13. #89076 | C22 | semidirect |
| 17. C22×C32×Q8 | D3 | semidirect |
| 34. C2×C32×Q8 | C2×D3 | semidirect |
| 50. C22×C3×Q8 | C3⋊D3 | semidirect |
| 67. C2×C33 | 2−1+4 | semidirect |
| 71. C2×C3×Q8 | C2×C3⋊D3 | semidirect |
| 91. C22×Q8 | C3⋊(C3⋊D3) | semidirect |
| 92. C33 | C2×2−1+4 | semidirect |
| 104. C2×C32 | #1007 | semidirect |
| 112. C2×Q8 | C2×C3⋊(C3⋊D3) | semidirect |
| 124. C32 | C2×#1007 | semidirect |
| 136. C2×C3 | #64364 | semidirect |
| 146. C3 | C2×#64364 | semidirect |
| 149. C2 | #11724682 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×Q8 | 2 |
| #11724682 | 2 |
| C2×#89080 | 2 |
| C2×Q8×C3⋊(C3⋊D3) | 2 |
| C2×#89076 | 2 |
| C2×#64364 | 3 |