Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
408 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 408 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 |
|---|---|---|
| 1. Q8×C9×Dic3 | C2 | semidirect |
| 4. #11720582 | C2 | semidirect |
| 6. #11720264 | C2 | semidirect |
| 7. Dic3×C9⋊C8 | C2 | semidirect |
| 15. C3×#3675 | C4 | semidirect |
| 39. C3×Q8×C9 | C2×C4 | semidirect |
| 50. C3×C9⋊C8 | C2×C4 | semidirect |
| 73. #3675 | Dic3 | direct (N × H) |
| 90. C9×Dic3 | SD16 | semidirect |
| 93. Q8×Dic3 | D9 | semidirect |
| 124. Q8×C9 | C2×Dic3 | semidirect |
| 139. C9⋊C8 | C2×Dic3 | semidirect |
| 206. C3×C9 | C4×SD16 | semidirect |
| 213. C3×Q8 | C4×D9 | semidirect |
| 290. Dic3 | #3675 | direct (N × H) |
| 293. C9 | Dic3×SD16 | semidirect |
| 296. Q8 | Dic3×D9 | semidirect |
| 331. C3 | C4×#3675 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C9×Dic3 | 2 |
| C2×C3×#3675 | 2 |
| Dic3×D36 | 2 |
| #11720582 | 2 |
| #11720266 | 2 |
| #11720264 | 2 |
| Dic3×C9⋊C8 | 2 |
| Dic3×#215 | 3 |
| C4×#3675 | 3 |