Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
440 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 92 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. C32×D3×Q8 | C2 | semidirect |
| 3. #88862 | C2 | semidirect |
| 4. C3×#3756 | C2 | semidirect |
| 5. #88798 | C2 | semidirect |
| 6. #88795 | C2 | semidirect |
| 7. #88786 | C2 | semidirect |
| 23. C3×D3×Q8 | D3 | semidirect |
| 26. #3756 | D3 | semidirect |
| 75. D3×Q8 | C3⋊D3 | semidirect |
| 106. C33 | #137 | semidirect |
| 165. C32 | #918 | semidirect |
| 166. C32 | #942 | semidirect |
| 194. C3 | #63948 | semidirect |
| 195. C3 | #64151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×D3×Q8 | 2 |
| #89022 | 2 |
| #88862 | 2 |
| C3×#3756 | 2 |
| #88798 | 2 |
| #88795 | 2 |
| #88786 | 2 |
| #64151 | 3 |
| #63948 | 3 |