Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
697 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 697 conjugacy classes of subgroups — too many to draw. Only its 118 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. M16×(C3⋊D3)⋊C3 | C2 | semidirect |
| 3. H(3,𝔽3)×#100 | C2 | semidirect |
| 4. #63660⋊C3 | C2 | semidirect |
| 5. #63650⋊C3 | C2 | semidirect |
| 6. C3⋊D3×#100 | C3 | semidirect |
| 15. M16×H(3,𝔽3) | C22 | semidirect |
| 16. #3748⋊C3 | C22 | semidirect |
| 21. M16×C3⋊D3 | C2×C3 | semidirect |
| 24. C32×#100 | D3 | semidirect |
| 25. C32×#100 | C2×C3 | semidirect |
| 26. #63660 | C2×C3 | semidirect |
| 27. #63650 | C2×C3 | semidirect |
| 64. C32×M16 | C2×D3 | semidirect |
| 65. C32×M16 | C22×C3 | semidirect |
| 66. #3748 | C22×C3 | semidirect |
| 140. (C3⋊D3)⋊C3 | #100 | direct (N × H) |
| 208. #100 | (C3⋊D3)⋊C3 | direct (N × H) |
| 209. H(3,𝔽3) | C2×#100 | semidirect |
| 270. C3⋊D3 | C3×#100 | semidirect |
| 283. M16 | C2×(C3⋊D3)⋊C3 | semidirect |
| 326. C32 | D3×#100 | semidirect |
| 327. C32 | C2×C3×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×(C3⋊D3)⋊C3 | 2 |
| M16×(C3⋊D3)⋊C3 | 2 |
| H(3,𝔽3)×#100 | 2 |
| #63660⋊C3 | 2 |
| #63650⋊C3 | 2 |
| C3⋊D3×#100 | 3 |
| C3×D3×#100 | 3 |