Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
528 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 528 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×C3×#3701 | C2 | semidirect |
| 2. C2×C9×#215 | C2 | semidirect |
| 3. #11721036 | C2 | semidirect |
| 4. C2×#88421 | C2 | semidirect |
| 5. #11720582 | C2 | semidirect |
| 6. #11720283 | C2 | semidirect |
| 7. (C2×D9)⋊(C3⋊C8) | C2 | semidirect |
| 29. C2×#3701 | D3 | semidirect |
| 44. C3×Q8×C9 | D4 | semidirect |
| 53. C3×D36 | D4 | semidirect |
| 113. C2×#215 | D9 | semidirect |
| 151. Q8×C9 | #67 | semidirect |
| 164. D36 | #67 | semidirect |
| 253. C3×C9 | #449 | semidirect |
| 264. C3×Q8 | #611 | semidirect |
| 367. C9 | #5238 | semidirect |
| 372. Q8 | #6194 | semidirect |
| 419. C3 | #10588852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3701 | 2 |
| C2×C9×#215 | 2 |
| #11721036 | 2 |
| C2×#88421 | 2 |
| #11720582 | 2 |
| #11720283 | 2 |
| (C2×D9)⋊(C3⋊C8) | 2 |
| #10591586 | 3 |
| #10588852 | 3 |