Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2156 conjugacy classes of subgroups; only the 363 normal subgroups are shown.
This group has 2156 conjugacy classes of subgroups — too many to draw. Only its 363 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 |
|---|---|---|
| 2. M16×C3⋊(C3⋊D3) | C2 | semidirect |
| 3. #11723913 | C2 | semidirect |
| 4. C33×#104 | C2 | semidirect |
| 5. #11722207 | C2 | semidirect |
| 6. #11722195 | C2 | semidirect |
| 7. #11722175 | C2 | semidirect |
| 10. #89080 | C4 | semidirect |
| 11. Q8×C3⋊(C3⋊D3) | C4 | semidirect |
| 13. #89078 | C4 | semidirect |
| 15. D4×C3⋊(C3⋊D3) | C4 | semidirect |
| 20. C33×M16 | C22 | semidirect |
| 21. C33×C42 | C22 | semidirect |
| 24. C4×C3⋊(C3⋊Dic3) | C22 | semidirect |
| 25. #88855 | C22 | semidirect |
| 31. C32×#104 | D3 | semidirect |
| 74. C32×M16 | C2×D3 | semidirect |
| 75. C32×C42 | C2×D3 | semidirect |
| 100. C3×#104 | C3⋊D3 | semidirect |
| 149. C3×M16 | C2×C3⋊D3 | semidirect |
| 150. C3×C42 | C2×C3⋊D3 | semidirect |
| 178. #104 | C3⋊(C3⋊D3) | semidirect |
| 179. C33 | #421 | semidirect |
| 226. M16 | C2×C3⋊(C3⋊D3) | semidirect |
| 231. C42 | C2×C3⋊(C3⋊D3) | semidirect |
| 247. C32 | #4821 | semidirect |
| 296. C3 | #10592520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×C3⋊(C3⋊D3) | 2 |
| M16×C3⋊(C3⋊D3) | 2 |
| #11723913 | 2 |
| C33×#104 | 2 |
| #11722207 | 2 |
| #11722195 | 2 |
| #11722175 | 2 |
| #10592520 | 3 |