Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. C2×#88427 | C2 | semidirect |
| 5. #11720297 | C2 | semidirect |
| 6. #11720268 | C2 | semidirect |
| 7. #11720265 | C2 | semidirect |
| 219. C3×C9 | #470 | semidirect |
| 313. C9 | #5052 | semidirect |
| 353. C3 | #10588728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88532 | 2 |
| C9×#924 | 2 |
| C3×#63486 | 2 |
| C2×#88427 | 2 |
| #11720297 | 2 |
| #11720268 | 2 |
| #11720265 | 2 |
| #10591189 | 3 |
| #10588728 | 3 |