Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
992 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 992 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. C3×#64083 | C2 | semidirect |
| 2. C32×C4×D12 | C2 | semidirect |
| 3. C2×#88789 | C2 | semidirect |
| 4. C4⋊(C3⋊(C3⋊(C3⋊C8))) | C2 | semidirect |
| 5. #11722033 | C2 | semidirect |
| 20. #64083 | D3 | semidirect |
| 22. C3×C4×D12 | D3 | semidirect |
| 40. C32×D12 | D4 | semidirect |
| 75. C33×C4 | D8 | semidirect |
| 84. C4×D12 | C3⋊D3 | semidirect |
| 117. C3×D12 | D12 | semidirect |
| 172. C32×C4 | #213 | semidirect |
| 173. C32×C4 | #213 | semidirect |
| 184. C33 | #459 | semidirect |
| 212. D12 | C4⋊(C3⋊D3) | semidirect |
| 262. C3×C4 | #3713 | semidirect |
| 263. C3×C4 | #3753 | semidirect |
| 270. C32 | #5015 | semidirect |
| 271. C32 | #5072 | semidirect |
| 308. C4 | #88789 | semidirect |
| 312. C3 | #10590347 | semidirect |
| 313. C3 | #10592714 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64083 | 2 |
| C32×C4×D12 | 2 |
| C2×#88789 | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| #11722033 | 2 |
| #10592714 | 3 |
| #10590347 | 3 |