Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
419 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 419 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#88529 | C2 | semidirect |
| 2. C2×#3745⋊C3 | C2 | semidirect |
| 3. C2×(C3⋊(C3⋊C16))⋊C3 | C2 | semidirect |
| 4. #11720253 | C2 | direct (N × H) |
| 11. #88529 | C22 | semidirect |
| 13. #3745⋊C3 | C22 | semidirect |
| 14. (C3⋊(C3⋊C16))⋊C3 | C22 | semidirect |
| 15. C2×#3745 | D3 | semidirect |
| 20. C2×C3⋊(C3⋊C16) | D3 | semidirect |
| 45. #3745 | C2×D3 | semidirect |
| 54. C3⋊(C3⋊C16) | C2×D3 | semidirect |
| 101. C2×H(3,𝔽3) | D16 | semidirect |
| 156. H(3,𝔽3) | C2×D16 | semidirect |
| 192. C2×C32 | D48 | semidirect |
| 193. C2×C32 | #826 | semidirect |
| 236. C32 | C2×D48 | semidirect |
| 237. C32 | C2×#826 | semidirect |
| 275. C2 | #11720253 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88529 | 2 |
| C2×#3745⋊C3 | 2 |
| C2×(C3⋊(C3⋊C16))⋊C3 | 2 |
| #11720253 | 2 |
| C2×#63546 | 3 |
| C2×#63545 | 3 |