Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1284 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 1284 conjugacy classes of subgroups — too many to draw. Only its 268 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. C3×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. C32×C4×C3⋊C8 | C2 | semidirect |
| 5. #11722021 | C2 | semidirect |
| 15. #88788 | C4 | direct (N × H) |
| 23. C4×C3⋊(C3⋊C8) | D3 | semidirect |
| 25. C3×C4×C3⋊C8 | D3 | semidirect |
| 34. C3×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 35. C32×C3⋊C8 | C2×C4 | semidirect |
| 62. C33×C4 | M16 | semidirect |
| 76. C4×C3⋊C8 | C3⋊D3 | semidirect |
| 99. C3⋊(C3⋊C8) | C4×D3 | semidirect |
| 101. C3×C3⋊C8 | C4×D3 | semidirect |
| 138. C32×C4 | ΓL(1,𝔽25) | semidirect |
| 139. C32×C4 | ΓL(1,𝔽25) | semidirect |
| 153. C33 | C4×M16 | semidirect |
| 178. C3⋊C8 | C4×C3⋊D3 | semidirect |
| 207. C3×C4 | #3712 | semidirect |
| 208. C3×C4 | #3743 | semidirect |
| 218. C32 | C4×ΓL(1,𝔽25) | semidirect |
| 219. C32 | C4×ΓL(1,𝔽25) | semidirect |
| 243. C4 | #88788 | direct (N × H) |
| 246. C3 | C4×#3712 | semidirect |
| 247. C3 | C4×#3743 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C3⋊(C3⋊D3) | 2 |
| C2×#88788 | 2 |
| C3×C4×C3⋊(C3⋊C8) | 2 |
| C32×C4×C3⋊C8 | 2 |
| #11722021 | 2 |
| C4×#3743 | 3 |
| C4×#3712 | 3 |