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. C2×C33×#41 | C2 | semidirect |
| 2. #11724685 | C2 | direct (N × H) |
| 3. C2×Q8×C3⋊(C3⋊D3) | C2 | semidirect |
| 4. C2×#89078 | C2 | semidirect |
| 5. C2×#89076 | C2 | semidirect |
| 6. C22×#6308 | C2 | semidirect |
| 8. C33×#41 | C22 | semidirect |
| 14. Q8×C3⋊(C3⋊D3) | C22 | semidirect |
| 15. #89078 | C22 | semidirect |
| 16. #89076 | C22 | semidirect |
| 21. C2×#6308 | C22 | semidirect |
| 22. C2×C32×#41 | D3 | semidirect |
| 43. C32×#41 | C2×D3 | semidirect |
| 65. C2×C3×#41 | C3⋊D3 | semidirect |
| 87. C2×C33 | 2−1+4 | semidirect |
| 90. C3×#41 | C2×C3⋊D3 | semidirect |
| 115. C2×#41 | C3⋊(C3⋊D3) | semidirect |
| 118. C33 | C2×2−1+4 | semidirect |
| 134. C2×C32 | #1010 | semidirect |
| 139. #41 | C2×C3⋊(C3⋊D3) | semidirect |
| 159. C32 | C2×#1010 | semidirect |
| 175. C2×C3 | #64367 | semidirect |
| 186. C3 | C2×#64367 | semidirect |
| 189. C2 | #11724685 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×#41 | 2 |
| #11724685 | 2 |
| C2×Q8×C3⋊(C3⋊D3) | 2 |
| C2×#89078 | 2 |
| C2×#89076 | 2 |
| C22×#6308 | 2 |
| C2×#64367 | 3 |