Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
513 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 513 conjugacy classes of subgroups — too many to draw. Only its 103 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×C8×(C3⋊D3)⋊C3 | C2 | semidirect |
| 3. C8×#1084 | C2 | semidirect |
| 4. #11720317 | C2 | semidirect |
| 5. #11720304 | C2 | semidirect |
| 16. C2×C8×C3⋊D3 | D3 | semidirect |
| 31. #6198 | C8 | direct (N × H) |
| 32. C8×H(3,𝔽3) | D4 | semidirect |
| 56. C2×(C3⋊D3)⋊C3 | C2×C8 | semidirect |
| 60. #1084 | C2×C8 | semidirect |
| 91. C32×C8 | #67 | semidirect |
| 130. C2×C3⋊D3 | D3×C8 | semidirect |
| 149. H(3,𝔽3) | C8×D4 | semidirect |
| 227. C32 | C8×#67 | semidirect |
| 238. C8 | #6198 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×(C3⋊D3)⋊C3 | 2 |
| C4×#6198 | 2 |
| C8×#1084 | 2 |
| #11720317 | 2 |
| #11720304 | 2 |
| C8×#626 | 3 |