Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
330 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 37. C3×Q8×C9 | Q8 | semidirect |
| 114. Q8×C9 | Dic6 | semidirect |
| 188. C3×C9 | #477 | semidirect |
| 193. C3×Q8 | Dic18 | semidirect |
| 264. C9 | #4793 | semidirect |
| 267. Q8 | #6189 | semidirect |
| 296. C3 | #10588703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C9×Dic3 | 2 |
| #11720970 | 2 |
| #11720582 | 2 |
| C3×#63395 | 2 |
| #11720263 | 2 |
| #11720262 | 2 |
| Dic3⋊(C9⋊C8) | 2 |
| #10591546 | 3 |
| #10588703 | 3 |