Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
670 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 93 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×D9×D12 | C2 | semidirect |
| 2. C2×#88544 | C2 | semidirect |
| 3. C3×#63500 | C2 | semidirect |
| 4. C2×C9×#213 | C2 | semidirect |
| 5. #11720294 | C2 | semidirect |
| 6. #11720284 | C2 | semidirect |
| 7. (C2×D9)⋊(C3⋊C8) | C2 | semidirect |
| 11. C2×C3×D4×C9 | C22 | semidirect |
| 20. C2×C3⋊(C9⋊C8) | C22 | semidirect |
| 23. C3×C4⋊Dic9 | C22 | semidirect |
| 24. C2×C9×C3⋊C8 | C22 | semidirect |
| 34. #63500 | D3 | semidirect |
| 51. C4⋊(C3⋊D9) | D4 | semidirect |
| 56. C9×D12 | D4 | semidirect |
| 82. C2×D4×C9 | C2×D3 | semidirect |
| 95. C4⋊Dic9 | C2×D3 | semidirect |
| 110. C2×C3×D9 | D8 | semidirect |
| 124. C2×#213 | D9 | semidirect |
| 196. C2×C3×D4 | C2×D9 | semidirect |
| 224. C2×C3⋊C8 | C2×D9 | semidirect |
| 263. C2×D9 | #213 | semidirect |
| 277. C3×C9 | #447 | semidirect |
| 322. D12 | #611 | semidirect |
| 356. C2×D4 | D3×D9 | semidirect |
| 411. C9 | #5036 | semidirect |
| 472. C3 | #10588836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D9×D12 | 2 |
| C2×#88544 | 2 |
| C3×#63500 | 2 |
| C2×C9×#213 | 2 |
| #11720294 | 2 |
| #11720284 | 2 |
| (C2×D9)⋊(C3⋊C8) | 2 |
| #10591515 | 3 |
| #10588836 | 3 |