Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
619 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 619 conjugacy classes of subgroups — too many to draw. Only its 123 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. #63630⋊C3 | C2 | semidirect |
| 4. #11720303 | C2 | semidirect |
| 12. #88434 | C4 | semidirect |
| 16. #63630 | D3 | semidirect |
| 26. (C3⋊(C3⋊C8))⋊C3 | C2×C4 | semidirect |
| 73. C3⋊(C3⋊C8) | C4×D3 | semidirect |
| 78. #272 | #97 | semidirect |
| 117. H(3,𝔽3) | C2×#97 | semidirect |
| 177. C32 | D3×#97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×#272 | 2 |
| C2×#88434 | 2 |
| #63630⋊C3 | 2 |
| #11720303 | 2 |
| D3×#803 | 3 |