Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
612 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 77 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. #11722478 | C2 | semidirect |
| 2. #11721840 | C2 | semidirect |
| 3. C9×#932 | C2 | semidirect |
| 4. C3×#63495 | C2 | semidirect |
| 5. #11720300 | C2 | semidirect |
| 6. #11720291 | C2 | semidirect |
| 7. #11720288 | C2 | semidirect |
| 10. C2×C3×D4×C9 | C22 | semidirect |
| 20. C4×C3⋊Dic9 | C22 | semidirect |
| 25. C9×#208 | C22 | semidirect |
| 26. C3×#3667 | C22 | semidirect |
| 38. #63495 | D3 | semidirect |
| 54. C9×D12 | D4 | semidirect |
| 56. C3×D36 | D4 | semidirect |
| 58. C9×Dic6 | D4 | semidirect |
| 59. C3×Dic18 | D4 | semidirect |
| 86. C2×D4×C9 | C2×D3 | semidirect |
| 104. #3667 | C2×D3 | semidirect |
| 126. #932 | D9 | semidirect |
| 182. D36 | #67 | semidirect |
| 185. Dic18 | #67 | semidirect |
| 198. C2×C3×D4 | C2×D9 | semidirect |
| 232. #208 | C2×D9 | semidirect |
| 274. C3×C9 | #453 | semidirect |
| 319. D12 | #611 | semidirect |
| 325. Dic6 | #611 | semidirect |
| 355. C2×D4 | D3×D9 | semidirect |
| 399. C9 | #5198 | semidirect |
| 453. C3 | #10588879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722478 | 2 |
| #11721840 | 2 |
| C9×#932 | 2 |
| C3×#63495 | 2 |
| #11720300 | 2 |
| #11720291 | 2 |
| #11720288 | 2 |
| #10591522 | 3 |
| #10588879 | 3 |