Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
704 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
| 2. C2×#88549 | C2 | semidirect |
| 4. #11720531 | C2 | semidirect |
| 5. C4⋊#6180 | C2 | semidirect |
| 17. C32×C4×Q8 | D3 | semidirect |
| 24. Q8×H(3,𝔽3) | D4 | semidirect |
| 54. C4×H(3,𝔽3) | SD16 | semidirect |
| 69. C32×Q8 | D12 | semidirect |
| 112. C32×C4 | #215 | semidirect |
| 117. C4×Q8 | #272 | semidirect |
| 120. H(3,𝔽3) | #460 | semidirect |
| 181. C32 | #5027 | semidirect |
| 184. Q8 | C4⋊#272 | semidirect |
| 210. C4 | #88549 | semidirect |
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 |
| #11721720 | 2 |
| #11720531 | 2 |
| C4⋊#6180 | 2 |
| C3×#5027 | 3 |