Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
440 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 99 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×#88523 | C2 | semidirect |
| 3. C2×D9×C3⋊C8 | C2 | semidirect |
| 4. C3×(C2×D9)⋊C8 | C2 | semidirect |
| 5. C9×Dic3⋊C8 | C2 | semidirect |
| 6. #11720282 | C2 | semidirect |
| 7. #11720258 | C2 | semidirect |
| 36. (C2×D9)⋊C8 | D3 | semidirect |
| 51. C3⋊(C9⋊C8) | D4 | semidirect |
| 92. C2×C3×D9 | M16 | semidirect |
| 112. Dic3⋊C8 | D9 | semidirect |
| 212. C2×D9 | ΓL(1,𝔽25) | semidirect |
| 229. C3×C9 | #435 | semidirect |
| 331. C9 | #4730 | semidirect |
| 376. C3 | #10588520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88523 | 2 |
| C4×#6192 | 2 |
| C2×D9×C3⋊C8 | 2 |
| C3×(C2×D9)⋊C8 | 2 |
| C9×Dic3⋊C8 | 2 |
| #11720282 | 2 |
| #11720258 | 2 |
| #10590907 | 3 |
| #10588520 | 3 |