Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1484 conjugacy classes of subgroups; only the 635 normal subgroups are shown.
This group has 1484 conjugacy classes of subgroups — too many to draw. Only its 635 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 |
|---|---|---|
| 4. #11722192 | C2 | direct (N × H) |
| 66. C2×C33 | #108 | semidirect |
| 90. C33 | C2×#108 | semidirect |
| 103. C2×C32 | #822 | semidirect |
| 123. C32 | C2×#822 | semidirect |
| 136. C2×C3 | #63649 | semidirect |
| 146. C3 | C2×#63649 | semidirect |
| 149. C2 | #11722192 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×M16 | 2 |
| C2×#88855 | 2 |
| C22×C3⋊(C3⋊(C3⋊C8)) | 2 |
| #11722192 | 2 |
| C2×#63649 | 3 |