Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
541 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 541 conjugacy classes of subgroups — too many to draw. Only its 188 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. C4×C8×H(3,𝔽3) | C2 | semidirect |
| 4. #63642⋊C3 | C2 | semidirect |
| 5. C4×(C3⋊(C3⋊C8))⋊C3 | C2 | semidirect |
| 6. C4×#3743 | C3 | semidirect |
| 15. #3743⋊C3 | C4 | direct (N × H) |
| 21. C32×C4×C8 | D3 | semidirect |
| 22. C32×C4×C8 | C2×C3 | semidirect |
| 23. #63642 | C2×C3 | semidirect |
| 24. C4×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 34. C8×H(3,𝔽3) | C2×C4 | semidirect |
| 35. (C3⋊(C3⋊C8))⋊C3 | C2×C4 | semidirect |
| 52. #3743 | C3×C4 | semidirect |
| 60. C4×H(3,𝔽3) | M16 | semidirect |
| 97. C32×C8 | C4×D3 | semidirect |
| 98. C32×C8 | C2×C3×C4 | semidirect |
| 99. C3⋊(C3⋊C8) | C2×C3×C4 | semidirect |
| 140. C32×C4 | ΓL(1,𝔽25) | semidirect |
| 141. C32×C4 | C3×M16 | semidirect |
| 152. C4×C8 | (C3⋊D3)⋊C3 | semidirect |
| 153. H(3,𝔽3) | C4×M16 | semidirect |
| 225. C32 | C4×ΓL(1,𝔽25) | semidirect |
| 226. C32 | C3×C4×M16 | semidirect |
| 235. C8 | C4×(C3⋊D3)⋊C3 | semidirect |
| 252. C4 | #3743⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3743⋊C3 | 2 |
| C42×(C3⋊D3)⋊C3 | 2 |
| C4×C8×H(3,𝔽3) | 2 |
| #63642⋊C3 | 2 |
| C4×(C3⋊(C3⋊C8))⋊C3 | 2 |
| C4×#3743 | 3 |
| C3×C4×ΓL(1,𝔽25) | 3 |