Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
869 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 869 conjugacy classes of subgroups — too many to draw. Only its 151 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. C22×Q8×H(3,𝔽3) | C2 | semidirect |
| 2. C2×#88549 | C2 | semidirect |
| 4. #11720583 | C2 | semidirect |
| 5. #11720573 | C2 | semidirect |
| 18. C22×C32×Q8 | D3 | semidirect |
| 27. Q8×H(3,𝔽3) | D4 | semidirect |
| 52. C22×H(3,𝔽3) | SD16 | semidirect |
| 75. C32×Q8 | #67 | semidirect |
| 115. C22×C32 | #215 | semidirect |
| 124. C22×Q8 | #272 | semidirect |
| 129. H(3,𝔽3) | #448 | semidirect |
| 196. C32 | #5227 | semidirect |
| 201. Q8 | #6235 | semidirect |
| 226. C22 | #88549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×H(3,𝔽3) | 2 |
| C2×#88549 | 2 |
| #11721830 | 2 |
| #11720583 | 2 |
| #11720573 | 2 |
| C3×#5227 | 3 |