Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1007 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1007 conjugacy classes of subgroups — too many to draw. Only its 155 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×#88652 | C2 | semidirect |
| 2. C2×#88529 | C2 | semidirect |
| 3. C2×C8×(C3⋊D3)⋊C3 | C2 | semidirect |
| 4. C2×#3746⋊C3 | C2 | semidirect |
| 5. C2×#88437 | C2 | semidirect |
| 6. #11720850 | C2 | direct (N × H) |
| 15. #88652 | C22 | semidirect |
| 17. #88529 | C22 | semidirect |
| 19. C8×(C3⋊D3)⋊C3 | C22 | semidirect |
| 20. #3746⋊C3 | C22 | semidirect |
| 21. #88437 | C22 | semidirect |
| 24. C2×#3746 | D3 | semidirect |
| 25. C2×C8×C3⋊D3 | D3 | semidirect |
| 72. #3746 | C2×D3 | semidirect |
| 73. C8×C3⋊D3 | C2×D3 | semidirect |
| 146. C2×H(3,𝔽3) | #135 | semidirect |
| 221. H(3,𝔽3) | C2×#135 | semidirect |
| 274. C2×C32 | #904 | semidirect |
| 275. C2×C32 | #919 | semidirect |
| 329. C32 | C2×#904 | semidirect |
| 330. C32 | C2×#919 | semidirect |
| 376. C2 | #11720850 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88652 | 2 |
| C2×#88529 | 2 |
| C2×C8×(C3⋊D3)⋊C3 | 2 |
| C2×#3746⋊C3 | 2 |
| C2×#88437 | 2 |
| #11720850 | 2 |
| C2×#63810 | 3 |
| C2×#63807 | 3 |