Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
710 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 231 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×#88524 | C2 | semidirect |
| 3. #11721706 | C2 | semidirect |
| 4. C3×C4×C8×C9 | C2 | semidirect |
| 21. C4×C8×C9 | D3 | semidirect |
| 29. C3×C8×C9 | D4 | semidirect |
| 49. C3×C4×C9 | SD16 | semidirect |
| 58. C3×C4×C8 | D9 | semidirect |
| 75. C8×C9 | D12 | semidirect |
| 103. C4×C9 | #204 | semidirect |
| 109. C4×C8 | C3⋊D9 | semidirect |
| 110. C3×C9 | #492 | semidirect |
| 125. C3×C8 | D36 | semidirect |
| 146. C3×C4 | #3664 | semidirect |
| 153. C9 | #4693 | semidirect |
| 161. C8 | C4⋊(C3⋊D9) | semidirect |
| 172. C4 | #88524 | semidirect |
| 174. C3 | #10588375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88524 | 2 |
| #11721711 | 2 |
| #11721706 | 2 |
| C3×C4×C8×C9 | 2 |
| #10592392 | 3 |
| #10588375 | 3 |