Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
456 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 55 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×#88810 | C2 | semidirect |
| 2. C2×C3×#3708 | C2 | semidirect |
| 3. #11722788 | C2 | direct (N × H) |
| 8. #88810 | C22 | semidirect |
| 9. C3×#3708 | C22 | semidirect |
| 12. C2×#3708 | D3 | semidirect |
| 31. #3708 | C2×D3 | semidirect |
| 61. C2×C33 | D16 | semidirect |
| 95. C33 | C2×D16 | semidirect |
| 119. C2×C32 | D48 | semidirect |
| 149. C32 | C2×D48 | semidirect |
| 161. C2×C3 | #63734 | semidirect |
| 173. C3 | C2×#63734 | semidirect |
| 175. C2 | #11722788 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88810 | 2 |
| C2×C3×#3708 | 2 |
| #11722788 | 2 |
| C2×#63734 | 3 |
| C2×D48 | 9 |