Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1852 conjugacy classes of subgroups; only the 276 normal subgroups are shown.
This group has 1852 conjugacy classes of subgroups — too many to draw. Only its 276 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 |
|---|---|---|
| 3. C2×C3×#3746 | C2 | semidirect |
| 4. C2×C32×Dic12 | C2 | semidirect |
| 5. C2×#88798 | C2 | semidirect |
| 6. #11723330 | C2 | direct (N × H) |
| 19. C3×#3746 | C22 | semidirect |
| 20. C32×Dic12 | C22 | semidirect |
| 21. #88798 | C22 | semidirect |
| 27. C2×#3746 | D3 | semidirect |
| 32. C2×C3×Dic12 | D3 | semidirect |
| 75. #3746 | C2×D3 | semidirect |
| 80. C3×Dic12 | C2×D3 | semidirect |
| 83. C2×C3⋊(C3⋊D3) | Q16 | semidirect |
| 99. C2×Dic12 | C3⋊D3 | semidirect |
| 141. C2×C33 | C2×Q16 | semidirect |
| 143. C3⋊(C3⋊D3) | C2×Q16 | semidirect |
| 170. Dic12 | C2×C3⋊D3 | semidirect |
| 202. C33 | C22×Q16 | semidirect |
| 242. C2×C32 | D3×Q16 | semidirect |
| 243. C2×C32 | D3×Q16 | semidirect |
| 285. C32 | C2×D3×Q16 | semidirect |
| 286. C32 | C2×D3×Q16 | semidirect |
| 304. C2×C3 | #63802 | semidirect |
| 305. C2×C3 | Q16×C3⋊D3 | semidirect |
| 320. C3 | C2×#63802 | semidirect |
| 321. C3 | C2×Q16×C3⋊D3 | semidirect |
| 323. C2 | #11723330 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89019 | 2 |
| C2×C8×C3⋊(C3⋊D3) | 2 |
| C2×C3×#3746 | 2 |
| C2×C32×Dic12 | 2 |
| C2×#88798 | 2 |
| #11723330 | 2 |
| C2×Q16×C3⋊D3 | 3 |
| C2×#63802 | 3 |