Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1168 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 158 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. #11723977 | C2 | semidirect |
| 2. C2×C3×#3753 | C2 | semidirect |
| 3. C2×C32×#213 | C2 | semidirect |
| 4. #11723529 | C2 | semidirect |
| 5. C2×#88796 | C2 | semidirect |
| 6. C2×#88794 | C2 | semidirect |
| 7. #11722021 | C2 | semidirect |
| 29. C2×#3753 | D3 | semidirect |
| 32. C2×C3×#213 | D3 | semidirect |
| 53. C3×C3⋊(C3⋊C8) | D4 | semidirect |
| 54. C32×C3⋊C8 | D4 | semidirect |
| 108. C2×#213 | C3⋊D3 | semidirect |
| 152. C3⋊(C3⋊C8) | #67 | semidirect |
| 154. C3×C3⋊C8 | #67 | semidirect |
| 227. C33 | #496 | semidirect |
| 269. C3⋊C8 | #638 | semidirect |
| 326. C32 | #5154 | semidirect |
| 327. C32 | #5154 | semidirect |
| 370. C3 | #10591485 | semidirect |
| 371. C3 | #10592853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723977 | 2 |
| C2×C3×#3753 | 2 |
| C2×C32×#213 | 2 |
| #11723529 | 2 |
| C2×#88796 | 2 |
| C2×#88794 | 2 |
| #11722021 | 2 |
| #10592853 | 3 |
| #10591485 | 3 |