Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
551 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 551 conjugacy classes of subgroups — too many to draw. Only its 184 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. H(3,𝔽3)×#97 | C2 | semidirect |
| 4. #63642⋊C3 | C2 | semidirect |
| 5. #63630⋊C3 | C2 | semidirect |
| 6. C3⋊D3×#97 | C3 | semidirect |
| 15. C8×(C3⋊D3)⋊C3 | C4 | semidirect |
| 21. C32×#97 | D3 | semidirect |
| 22. C32×#97 | C2×C3 | semidirect |
| 23. #63642 | C2×C3 | semidirect |
| 24. #63630 | C2×C3 | semidirect |
| 34. C8×H(3,𝔽3) | C2×C4 | semidirect |
| 35. (C3⋊(C3⋊C8))⋊C3 | C2×C4 | semidirect |
| 52. C8×C3⋊D3 | C3×C4 | semidirect |
| 97. C32×C8 | C4×D3 | semidirect |
| 98. C32×C8 | C2×C3×C4 | semidirect |
| 99. C3⋊(C3⋊C8) | C2×C3×C4 | semidirect |
| 104. (C3⋊D3)⋊C3 | #97 | direct (N × H) |
| 152. #97 | (C3⋊D3)⋊C3 | direct (N × H) |
| 153. H(3,𝔽3) | C2×#97 | semidirect |
| 190. C3⋊D3 | C3×#97 | semidirect |
| 225. C32 | D3×#97 | semidirect |
| 226. C32 | C2×C3×#97 | semidirect |
| 235. C8 | C4×(C3⋊D3)⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×(C3⋊D3)⋊C3 | 2 |
| C42×(C3⋊D3)⋊C3 | 2 |
| H(3,𝔽3)×#97 | 2 |
| #63642⋊C3 | 2 |
| #63630⋊C3 | 2 |
| C3⋊D3×#97 | 3 |
| C3×D3×#97 | 3 |