Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
792 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 137 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×#88529 | C2 | semidirect |
| 2. C2×#88528 | C2 | semidirect |
| 3. #11721721 | C2 | semidirect |
| 4. #11721720 | C2 | semidirect |
| 5. H(3,𝔽3)×#97 | C2 | semidirect |
| 20. C32×#97 | D3 | semidirect |
| 31. C8×H(3,𝔽3) | D4 | semidirect |
| 71. C32×C8 | D12 | semidirect |
| 107. #97 | #272 | semidirect |
| 108. H(3,𝔽3) | #496 | semidirect |
| 160. C32 | #4712 | semidirect |
| 171. 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 |
| C2×#88528 | 2 |
| #11721721 | 2 |
| #11721720 | 2 |
| H(3,𝔽3)×#97 | 2 |
| C3×#4712 | 3 |