Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1272 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 1272 conjugacy classes of subgroups — too many to draw. Only its 200 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. #11723915 | C2 | semidirect |
| 2. C32×C4×D12 | C2 | semidirect |
| 3. C2×#88790 | C2 | semidirect |
| 4. C3×C4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 5. #11722035 | C2 | semidirect |
| 23. C3×C4×D12 | D3 | semidirect |
| 26. C4⋊(C3⋊(C3⋊C8)) | D3 | semidirect |
| 40. C32×D12 | D4 | semidirect |
| 77. C33×C4 | D8 | semidirect |
| 87. C4×D12 | C3⋊D3 | semidirect |
| 124. C3×D12 | D12 | semidirect |
| 183. C32×C4 | D24 | semidirect |
| 184. C32×C4 | #213 | semidirect |
| 195. C33 | #459 | semidirect |
| 228. D12 | C4⋊(C3⋊D3) | semidirect |
| 281. C3×C4 | #3714 | semidirect |
| 282. C3×C4 | #3753 | semidirect |
| 289. C32 | #4843 | semidirect |
| 290. C32 | #5015 | semidirect |
| 328. C4 | #88790 | semidirect |
| 332. C3 | #10590349 | semidirect |
| 333. C3 | #10592714 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723915 | 2 |
| C32×C4×D12 | 2 |
| C2×#88790 | 2 |
| C3×C4⋊(C3⋊(C3⋊C8)) | 2 |
| #11722035 | 2 |
| #10592714 | 3 |
| #10590349 | 3 |