Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1298 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1298 conjugacy classes of subgroups — too many to draw. Only its 219 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. H(3,𝔽3)×C4⋊Q8 | C2 | semidirect |
| 2. #11721864 | C2 | semidirect |
| 3. #11721763 | C2 | semidirect |
| 4. #11721760 | C2 | semidirect |
| 5. C4×C4⋊#272 | C2 | semidirect |
| 17. C32×C4⋊Q8 | D3 | semidirect |
| 102. C4⋊Q8 | #272 | semidirect |
| 107. H(3,𝔽3) | #555 | semidirect |
| 155. C32 | #5734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×C4⋊Q8 | 2 |
| #11721864 | 2 |
| #11721763 | 2 |
| #11721760 | 2 |
| C4×C4⋊#272 | 2 |
| C3×#5734 | 3 |