Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1428 conjugacy classes of subgroups; only the 363 normal subgroups are shown.
This group has 1428 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 |
|---|---|---|
| 3. C33×#108 | C2 | semidirect |
| 4. #11722192 | C2 | semidirect |
| 5. #11722189 | C2 | semidirect |
| 17. C32×#108 | D3 | semidirect |
| 46. C3×#108 | C3⋊D3 | semidirect |
| 80. #108 | C3⋊(C3⋊D3) | semidirect |
| 81. C33 | #430 | semidirect |
| 108. C32 | #4893 | semidirect |
| 127. C3 | #10592592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M16×C3⋊(C3⋊D3) | 2 |
| C2×#88850 | 2 |
| C33×#108 | 2 |
| #11722192 | 2 |
| #11722189 | 2 |
| #10592592 | 3 |