Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
452 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 97 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×#88548 | C2 | semidirect |
| 2. C3×Q8×Dic9 | C2 | semidirect |
| 3. C2×C9×#215 | C2 | semidirect |
| 5. #11720294 | C2 | semidirect |
| 6. #11720284 | C2 | semidirect |
| 7. Dic9⋊(C3⋊C8) | C2 | semidirect |
| 31. Q8×Dic9 | D3 | semidirect |
| 41. C3×Q8×C9 | D4 | semidirect |
| 99. C3×Dic9 | SD16 | semidirect |
| 106. C2×#215 | D9 | semidirect |
| 138. Q8×C9 | D12 | semidirect |
| 225. Dic9 | #215 | semidirect |
| 233. C3×C9 | #460 | semidirect |
| 243. C3×Q8 | #611 | semidirect |
| 338. C9 | #5027 | semidirect |
| 342. Q8 | #6195 | semidirect |
| 384. C3 | #10588843 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88548 | 2 |
| C3×Q8×Dic9 | 2 |
| C2×C9×#215 | 2 |
| #11721040 | 2 |
| #11720294 | 2 |
| #11720284 | 2 |
| Dic9⋊(C3⋊C8) | 2 |
| #10591617 | 3 |
| #10588843 | 3 |