Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1960 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 1960 conjugacy classes of subgroups — too many to draw. Only its 407 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. C2×C33×D8 | C2 | semidirect |
| 2. #11723981 | C2 | semidirect |
| 3. D4×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 4. C2×#88860 | C2 | semidirect |
| 5. #11722202 | C2 | semidirect |
| 6. #11722191 | C2 | semidirect |
| 7. #11722184 | C2 | semidirect |
| 22. C2×C32×D8 | D3 | semidirect |
| 35. C33×D4 | D4 | semidirect |
| 75. C3⋊(C3⋊Dic3) | D8 | semidirect |
| 76. C2×C3×D8 | C3⋊D3 | semidirect |
| 89. C32×D4 | #67 | semidirect |
| 137. C2×D8 | C3⋊(C3⋊D3) | semidirect |
| 143. C33 | #459 | semidirect |
| 150. C3×D4 | #638 | semidirect |
| 196. C32 | #5150 | semidirect |
| 207. D4 | #6312 | semidirect |
| 236. C3 | #10592849 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D8 | 2 |
| #11723981 | 2 |
| D4×C3⋊(C3⋊Dic3) | 2 |
| C2×#88860 | 2 |
| #11722202 | 2 |
| #11722191 | 2 |
| #11722184 | 2 |
| #10592849 | 3 |