Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1344 conjugacy classes of subgroups; only the 627 normal subgroups are shown.
This group has 1344 conjugacy classes of subgroups — too many to draw. Only its 627 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. C4⋊(C3⋊(C3⋊(C3⋊C8))) | C2 | semidirect |
| 4. #11722173 | C2 | semidirect |
| 5. C4×C3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 78. C33 | #433 | semidirect |
| 104. C32 | #5000 | semidirect |
| 123. C3 | #10592699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#117 | 2 |
| #11722200 | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| #11722173 | 2 |
| C4×C3⋊(C3⋊(C3⋊C8)) | 2 |
| #10592699 | 3 |