Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1372 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 1372 conjugacy classes of subgroups — too many to draw. Only its 451 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. #11722200 | C2 | semidirect |
| 15. C23×C33 | C8 | semidirect |
| 46. C23×C32 | C3⋊C8 | semidirect |
| 79. C33 | #323 | semidirect |
| 84. C23×C3 | C3⋊(C3⋊C8) | semidirect |
| 114. C32 | #4525 | semidirect |
| 119. C23 | C3⋊(C3⋊(C3⋊C8)) | semidirect |
| 144. C3 | #10589391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×C22⋊C4 | 2 |
| #11722200 | 2 |
| #10589391 | 3 |