Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
402 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. Dic3×Dic18 | C2 | semidirect |
| 4. #11720540 | C2 | semidirect |
| 5. C8×C9×Dic3 | C2 | semidirect |
| 7. #11720276 | C2 | semidirect |
| 18. C3×#3664 | C4 | semidirect |
| 47. C3×Dic18 | C2×C4 | semidirect |
| 49. C3×C8×C9 | C2×C4 | semidirect |
| 79. #3664 | Dic3 | direct (N × H) |
| 89. C9×Dic3 | SD16 | semidirect |
| 105. C8×Dic3 | D9 | semidirect |
| 134. Dic18 | C2×Dic3 | semidirect |
| 137. C8×C9 | C2×Dic3 | semidirect |
| 204. C3×C9 | C4×SD16 | semidirect |
| 234. C3×C8 | C4×D9 | semidirect |
| 286. Dic3 | #3664 | direct (N × H) |
| 289. C9 | Dic3×SD16 | semidirect |
| 303. C8 | Dic3×D9 | semidirect |
| 327. C3 | C4×#3664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3664 | 2 |
| Dic3×D36 | 2 |
| Dic3×Dic18 | 2 |
| #11720540 | 2 |
| C8×C9×Dic3 | 2 |
| #11720283 | 2 |
| #11720276 | 2 |
| Dic3×#204 | 3 |
| C4×#3664 | 3 |