Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
551 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 551 conjugacy classes of subgroups — too many to draw. Only its 143 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. #11720520 | C2 | semidirect |
| 4. #63630⋊C3 | C2 | semidirect |
| 5. #11720312 | C2 | semidirect |
| 15. ((C3⋊D3)⋊C3)⋊C8 | C4 | semidirect |
| 20. #63630 | D3 | semidirect |
| 34. #6180 | C2×C4 | semidirect |
| 35. (C3⋊(C3⋊C8))⋊C3 | C2×C4 | semidirect |
| 96. C3⋊(C3⋊C8) | C4×D3 | semidirect |
| 104. (C3⋊D3)⋊C3 | #97 | semidirect |
| 153. H(3,𝔽3) | C2×#97 | semidirect |
| 190. C3⋊D3 | #803 | semidirect |
| 225. C32 | D3×#97 | semidirect |
| 226. C32 | C2×#803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×(C3⋊D3)⋊C3 | 2 |
| C2×((C3⋊D3)⋊C3)⋊C8 | 2 |
| #11720520 | 2 |
| #63630⋊C3 | 2 |
| #11720312 | 2 |
| #10590322 | 3 |
| D3×#803 | 3 |