Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1900 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 1900 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 |
|---|---|---|
| 1. C2×#89015 | C2 | semidirect |
| 2. C2×C8×C3⋊(C3⋊D3) | C2 | semidirect |
| 3. C2×C3×#3746 | C2 | semidirect |
| 4. C2×C32×D24 | C2 | semidirect |
| 5. C2×#88792 | C2 | semidirect |
| 6. #11723343 | C2 | direct (N × H) |
| 15. #89015 | C22 | semidirect |
| 18. C8×C3⋊(C3⋊D3) | C22 | semidirect |
| 19. C3×#3746 | C22 | semidirect |
| 20. C32×D24 | C22 | semidirect |
| 21. #88792 | C22 | semidirect |
| 27. C2×#3746 | D3 | semidirect |
| 32. C2×C3×D24 | D3 | semidirect |
| 75. #3746 | C2×D3 | semidirect |
| 80. C3×D24 | C2×D3 | semidirect |
| 100. C2×D24 | C3⋊D3 | semidirect |
| 142. C2×C33 | #135 | semidirect |
| 172. D24 | C2×C3⋊D3 | semidirect |
| 206. C33 | C2×#135 | semidirect |
| 247. C2×C32 | #912 | semidirect |
| 248. C2×C32 | #919 | semidirect |
| 293. C32 | C2×#912 | semidirect |
| 294. C32 | C2×#919 | semidirect |
| 313. C2×C3 | #63810 | semidirect |
| 314. C2×C3 | #64121 | semidirect |
| 331. C3 | C2×#63810 | semidirect |
| 332. C3 | C2×#64121 | semidirect |
| 335. C2 | #11723343 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89015 | 2 |
| C2×C8×C3⋊(C3⋊D3) | 2 |
| C2×C3×#3746 | 2 |
| C2×C32×D24 | 2 |
| C2×#88792 | 2 |
| #11723343 | 2 |
| C2×#64121 | 3 |
| C2×#63810 | 3 |