Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1088 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 148 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. C32×#951 | C2 | semidirect |
| 3. #11723436 | C2 | semidirect |
| 4. #11723375 | C2 | semidirect |
| 5. #11722207 | C2 | semidirect |
| 6. #11722045 | C2 | semidirect |
| 7. #11722026 | C2 | semidirect |
| 18. C2×C32×Dic6 | C22 | semidirect |
| 19. C4×C3⋊(C3⋊Dic3) | C22 | semidirect |
| 20. #88855 | C22 | semidirect |
| 23. C32×#208 | C22 | semidirect |
| 32. C3×#951 | D3 | semidirect |
| 84. C2×C3×Dic6 | C2×D3 | semidirect |
| 99. C3×#208 | C2×D3 | semidirect |
| 119. #951 | C3⋊D3 | semidirect |
| 205. C2×Dic6 | C2×C3⋊D3 | semidirect |
| 223. #208 | C2×C3⋊D3 | semidirect |
| 261. C33 | #455 | semidirect |
| 374. C32 | #5202 | semidirect |
| 375. C32 | #5242 | semidirect |
| 424. C3 | #10591664 | semidirect |
| 425. C3 | #10592901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64366 | 2 |
| C32×#951 | 2 |
| #11723436 | 2 |
| #11723375 | 2 |
| #11722207 | 2 |
| #11722045 | 2 |
| #11722026 | 2 |
| #10592901 | 3 |
| #10591664 | 3 |