Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3724 conjugacy classes of subgroups; only the 675 normal subgroups are shown.
This group has 3724 conjugacy classes of subgroups — too many to draw. Only its 675 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×#89080 | C2 | semidirect |
| 2. C2×C33×Q16 | C2 | semidirect |
| 3. C2×#88862 | C2 | semidirect |
| 4. #11723960 | C2 | direct (N × H) |
| 5. C2×#88852 | C2 | semidirect |
| 6. C2×C8×C3⋊(C3⋊D3) | C2 | semidirect |
| 10. #89080 | C22 | semidirect |
| 15. C33×Q16 | C22 | semidirect |
| 17. #88862 | C22 | semidirect |
| 19. #88852 | C22 | semidirect |
| 20. C8×C3⋊(C3⋊D3) | C22 | semidirect |
| 22. C2×C32×Q16 | D3 | semidirect |
| 50. C32×Q16 | C2×D3 | semidirect |
| 66. C2×C3×Q16 | C3⋊D3 | semidirect |
| 87. C2×C33 | #135 | semidirect |
| 98. C3×Q16 | C2×C3⋊D3 | semidirect |
| 115. C2×Q16 | C3⋊(C3⋊D3) | semidirect |
| 119. C33 | C2×#135 | semidirect |
| 135. C2×C32 | #919 | semidirect |
| 146. Q16 | C2×C3⋊(C3⋊D3) | semidirect |
| 161. C32 | C2×#919 | semidirect |
| 177. C2×C3 | #64128 | semidirect |
| 190. C3 | C2×#64128 | semidirect |
| 193. C2 | #11723960 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89080 | 2 |
| C2×C33×Q16 | 2 |
| C2×#88862 | 2 |
| #11723960 | 2 |
| C2×#88852 | 2 |
| C2×C8×C3⋊(C3⋊D3) | 2 |
| C2×#64128 | 3 |