Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
726 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 131 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. C4×C4⋊#272 | C2 | semidirect |
| 3. H(3,𝔽3)×#97 | C2 | semidirect |
| 4. #11720554 | C2 | semidirect |
| 5. #11720550 | C2 | semidirect |
| 14. #88529 | C4 | semidirect |
| 17. C32×#97 | D3 | semidirect |
| 25. C4⋊#272 | C2×C4 | semidirect |
| 28. C8×H(3,𝔽3) | C2×C4 | semidirect |
| 65. C32×C8 | C4×D3 | semidirect |
| 98. #97 | #272 | semidirect |
| 99. H(3,𝔽3) | #442 | semidirect |
| 145. C32 | #4711 | semidirect |
| 154. C8 | C4×#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88529 | 2 |
| C4×C4⋊#272 | 2 |
| H(3,𝔽3)×#97 | 2 |
| #11720554 | 2 |
| #11720550 | 2 |
| C3×#4711 | 3 |