Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
671 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 671 conjugacy classes of subgroups — too many to draw. Only its 133 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×#88527 | C2 | semidirect |
| 3. H(3,𝔽3)×C4⋊C8 | C2 | semidirect |
| 4. #11720553 | C2 | semidirect |
| 5. C4×#6180 | C2 | semidirect |
| 18. C32×C4⋊C8 | D3 | semidirect |
| 31. #6180 | D4 | semidirect |
| 48. C4×H(3,𝔽3) | M16 | semidirect |
| 101. C32×C4 | ΓL(1,𝔽25) | semidirect |
| 107. C4⋊C8 | #272 | semidirect |
| 110. H(3,𝔽3) | #436 | semidirect |
| 164. C32 | #4838 | semidirect |
| 190. C4 | #88527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88527 | 2 |
| C4×C4⋊#272 | 2 |
| H(3,𝔽3)×C4⋊C8 | 2 |
| #11720553 | 2 |
| C4×#6180 | 2 |
| C3×#4838 | 3 |