Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
516 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 101 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×Q8×D9 | C2 | semidirect |
| 2. C2×C9×#215 | C2 | semidirect |
| 4. C2×#88423 | C2 | semidirect |
| 5. #11720582 | C2 | semidirect |
| 6. (C2×D9)⋊(C3⋊C8) | C2 | semidirect |
| 7. #11720276 | C2 | semidirect |
| 29. C2×Q8×D9 | D3 | semidirect |
| 43. C3×Q8×C9 | D4 | semidirect |
| 56. C3×Dic18 | D4 | semidirect |
| 101. C2×C3×D9 | SD16 | semidirect |
| 112. C2×#215 | D9 | semidirect |
| 148. Q8×C9 | #67 | semidirect |
| 165. Dic18 | #67 | semidirect |
| 228. C2×D9 | #215 | semidirect |
| 246. C3×C9 | #448 | semidirect |
| 258. C3×Q8 | #611 | semidirect |
| 354. C9 | #5227 | semidirect |
| 361. Q8 | #6194 | semidirect |
| 402. C3 | #10588850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×D9 | 2 |
| C2×C9×#215 | 2 |
| #11721036 | 2 |
| C2×#88423 | 2 |
| #11720582 | 2 |
| (C2×D9)⋊(C3⋊C8) | 2 |
| #11720276 | 2 |
| #10591583 | 3 |
| #10588850 | 3 |