Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1000 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 1000 conjugacy classes of subgroups — too many to draw. Only its 186 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. C4×#6308 | C2 | semidirect |
| 4. C3×#63630 | C2 | semidirect |
| 5. #11722057 | C2 | semidirect |
| 6. #11722041 | C2 | semidirect |
| 21. #88794 | C4 | semidirect |
| 32. #63630 | D3 | semidirect |
| 44. #6308 | C2×C4 | semidirect |
| 50. C3×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 140. C3⋊(C3⋊C8) | C4×D3 | semidirect |
| 213. C33 | #440 | semidirect |
| 302. C32 | #4710 | semidirect |
| 303. C32 | #5018 | semidirect |
| 341. C3 | #10590360 | semidirect |
| 342. C3 | #10592717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6308 | 2 |
| C32×C4×D12 | 2 |
| C2×#88794 | 2 |
| C3×#63630 | 2 |
| #11722057 | 2 |
| #11722041 | 2 |
| #11722032 | 2 |
| #10592717 | 3 |
| #10590360 | 3 |