Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
496 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 496 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×#88544 | C2 | semidirect |
| 2. C3×D4×Dic9 | C2 | semidirect |
| 3. C2×C9×#213 | C2 | semidirect |
| 4. #11721040 | C2 | semidirect |
| 5. #11720294 | C2 | semidirect |
| 6. #11720284 | C2 | semidirect |
| 7. Dic9⋊(C3⋊C8) | C2 | semidirect |
| 32. D4×Dic9 | D3 | semidirect |
| 42. C3×D4×C9 | D4 | semidirect |
| 102. C3×Dic9 | D8 | semidirect |
| 110. C2×#213 | D9 | semidirect |
| 146. D4×C9 | D12 | semidirect |
| 237. Dic9 | #213 | semidirect |
| 245. C3×C9 | #459 | semidirect |
| 260. C3×D4 | #611 | semidirect |
| 361. C9 | #5015 | semidirect |
| 372. D4 | #6195 | semidirect |
| 413. C3 | #10588830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88544 | 2 |
| C3×D4×Dic9 | 2 |
| C2×C9×#213 | 2 |
| #11721040 | 2 |
| #11720294 | 2 |
| #11720284 | 2 |
| Dic9⋊(C3⋊C8) | 2 |
| #10591481 | 3 |
| #10588830 | 3 |