Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
516 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 107 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×D3×Q8×C9 | C2 | semidirect |
| 2. C2×C3×#3675 | C2 | semidirect |
| 4. C2×#88425 | C2 | semidirect |
| 5. #11720582 | C2 | semidirect |
| 6. #11720298 | C2 | semidirect |
| 7. (C2×D3)⋊(C9⋊C8) | C2 | semidirect |
| 34. C2×#3675 | D3 | semidirect |
| 43. C3×Q8×C9 | D4 | semidirect |
| 56. C9×Dic6 | D4 | semidirect |
| 98. C2×D3×C9 | SD16 | semidirect |
| 109. C2×D3×Q8 | D9 | semidirect |
| 151. Q8×C9 | #67 | semidirect |
| 246. C3×C9 | #448 | semidirect |
| 258. C3×Q8 | #611 | semidirect |
| 287. Dic6 | #611 | semidirect |
| 335. C2×D3 | #3675 | semidirect |
| 354. C9 | #5170 | semidirect |
| 361. Q8 | #6194 | semidirect |
| 402. C3 | #10588908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Q8×C9 | 2 |
| C2×C3×#3675 | 2 |
| #11721037 | 2 |
| C2×#88425 | 2 |
| #11720582 | 2 |
| #11720298 | 2 |
| (C2×D3)⋊(C9⋊C8) | 2 |
| #10591583 | 3 |
| #10588908 | 3 |