Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
930 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 242 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 |
|---|---|---|
| 1. #11722639 | C2 | semidirect |
| 2. H(3,𝔽3)×#131 | C2 | semidirect |
| 3. #64118⋊C3 | C2 | semidirect |
| 4. #64113⋊C3 | C2 | semidirect |
| 5. C2×#3746⋊C3 | C2 | semidirect |
| 6. #10596224 | C3 | semidirect |
| 19. #64367 | C2×C3 | semidirect |
| 22. C32×#131 | D3 | semidirect |
| 23. C32×#131 | C2×C3 | semidirect |
| 24. #64118 | C2×C3 | semidirect |
| 25. C2×#3746 | C2×C3 | semidirect |
| 26. #64113 | C2×C3 | semidirect |
| 174. #131 | (C3⋊D3)⋊C3 | semidirect |
| 175. H(3,𝔽3) | #578 | semidirect |
| 252. C32 | #5753 | semidirect |
| 253. C32 | C3×#578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722639 | 2 |
| H(3,𝔽3)×#131 | 2 |
| #64118⋊C3 | 2 |
| #64113⋊C3 | 2 |
| C2×#3746⋊C3 | 2 |
| #10596224 | 3 |
| C3×#5753 | 3 |