Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
671 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 671 conjugacy classes of subgroups — too many to draw. Only its 145 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. C4×Q8×H(3,𝔽3) | C2 | semidirect |
| 4. #11720583 | C2 | semidirect |
| 6. #11720530 | C2 | semidirect |
| 7. C4×#6180 | C2 | semidirect |
| 16. #88549 | C4 | direct (N × H) |
| 21. C32×C4×Q8 | D3 | semidirect |
| 30. Q8×H(3,𝔽3) | C2×C4 | semidirect |
| 41. #6180 | C2×C4 | semidirect |
| 63. C4×H(3,𝔽3) | SD16 | semidirect |
| 83. C32×Q8 | C4×D3 | semidirect |
| 131. C32×C4 | #215 | semidirect |
| 136. C4×Q8 | #272 | semidirect |
| 142. H(3,𝔽3) | C4×SD16 | semidirect |
| 209. C32 | C4×#215 | semidirect |
| 212. Q8 | C4×#272 | semidirect |
| 240. C4 | #88549 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×H(3,𝔽3) | 2 |
| C2×#88549 | 2 |
| C4×C4⋊#272 | 2 |
| #11720583 | 2 |
| #11720531 | 2 |
| #11720530 | 2 |
| C4×#6180 | 2 |
| C3×C4×#215 | 3 |