Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1279 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 1279 conjugacy classes of subgroups — too many to draw. Only its 227 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 |
|---|---|---|
| 2. C2×#3748⋊C3 | C2 | semidirect |
| 3. C2×#88435 | C2 | semidirect |
| 4. #11721065 | C2 | direct (N × H) |
| 5. C2×#88434 | C2 | semidirect |
| 16. #3748⋊C3 | C22 | semidirect |
| 17. C2×(C3⋊(C3⋊C8))⋊C3 | C22 | semidirect |
| 18. #88435 | C22 | semidirect |
| 19. #88434 | C22 | semidirect |
| 22. C2×#3748 | D3 | semidirect |
| 45. (C3⋊(C3⋊C8))⋊C3 | C23 | semidirect |
| 66. #3748 | C2×D3 | semidirect |
| 67. C2×C3⋊(C3⋊C8) | C2×D3 | semidirect |
| 77. C2×#272 | M16 | semidirect |
| 133. C3⋊(C3⋊C8) | C22×D3 | semidirect |
| 137. C2×H(3,𝔽3) | C2×M16 | semidirect |
| 140. #272 | C2×M16 | semidirect |
| 209. H(3,𝔽3) | C22×M16 | semidirect |
| 271. C2×C32 | D3×M16 | semidirect |
| 330. C32 | C2×D3×M16 | semidirect |
| 384. C2 | #11721065 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#272 | 2 |
| C2×#3748⋊C3 | 2 |
| C2×#88435 | 2 |
| #11721065 | 2 |
| C2×#88434 | 2 |
| C2×D3×#208 | 3 |