Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1184 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 1184 conjugacy classes of subgroups — too many to draw. Only its 188 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. C2×#88861 | C2 | semidirect |
| 3. #11723426 | C2 | semidirect |
| 4. C2×#88799 | C2 | semidirect |
| 5. C3×#63659 | C2 | semidirect |
| 6. #11722037 | C2 | semidirect |
| 7. (C2×D3)⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 35. #63659 | D3 | semidirect |
| 249. C33 | #452 | semidirect |
| 359. C32 | #4783 | semidirect |
| 360. C32 | #5239 | semidirect |
| 408. C3 | #10591463 | semidirect |
| 409. C3 | #10592938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#237 | 2 |
| C2×#88861 | 2 |
| #11723426 | 2 |
| C2×#88799 | 2 |
| C3×#63659 | 2 |
| #11722037 | 2 |
| (C2×D3)⋊(C3⋊(C3⋊C8)) | 2 |
| #10592938 | 3 |
| #10591463 | 3 |