Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2172 conjugacy classes of subgroups; only the 336 normal subgroups are shown.
This group has 2172 conjugacy classes of subgroups — too many to draw. Only its 336 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 |
|---|---|---|
| 3. C3×#64078 | C2 | semidirect |
| 4. C32×#869 | C2 | semidirect |
| 5. #11723536 | C2 | semidirect |
| 7. #11723451 | C2 | semidirect |
| 32. #64078 | D3 | semidirect |
| 34. C3×#869 | D3 | semidirect |
| 44. C4×C3⋊(C3⋊D3) | Q8 | semidirect |
| 88. C33×C4 | C2×Q8 | semidirect |
| 90. C3⋊(C3⋊Dic3) | C2×Q8 | semidirect |
| 107. #869 | C3⋊D3 | semidirect |
| 144. C3⋊(C3⋊D3) | C4⋊Q8 | semidirect |
| 190. C32×C4 | D3×Q8 | semidirect |
| 191. C32×C4 | D3×Q8 | semidirect |
| 208. C33 | C2×C4⋊Q8 | semidirect |
| 277. C3×C4 | #3797 | semidirect |
| 280. C3×C4 | Q8×C3⋊D3 | semidirect |
| 290. C32 | D3×C4⋊Q8 | semidirect |
| 291. C32 | D3×C4⋊Q8 | semidirect |
| 321. C4 | #89019 | semidirect |
| 324. C3 | #10593909 | semidirect |
| 325. C3 | C3⋊D3×C4⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89019 | 2 |
| C42×C3⋊(C3⋊D3) | 2 |
| C3×#64078 | 2 |
| C32×#869 | 2 |
| #11723536 | 2 |
| #11723503 | 2 |
| #11723451 | 2 |
| C3⋊D3×C4⋊Q8 | 3 |
| #10593909 | 3 |