Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
624 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 104 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×C4⋊(C3⋊(C3⋊D3)) | C2 | semidirect |
| 2. C3×#3828 | C2 | semidirect |
| 3. C32×#208 | C2 | semidirect |
| 4. #88797 | C2 | semidirect |
| 5. #88791 | C2 | semidirect |
| 13. C3×C4⋊(C3⋊D3) | C22 | semidirect |
| 15. C3×#634 | C22 | semidirect |
| 16. C32×C3⋊C8 | C22 | semidirect |
| 17. #3828 | D3 | semidirect |
| 25. C3×#208 | D3 | semidirect |
| 50. C4⋊(C3⋊D3) | C2×D3 | semidirect |
| 52. #634 | C2×D3 | semidirect |
| 58. C3×C3⋊C8 | C2×D3 | semidirect |
| 71. #208 | C3⋊D3 | semidirect |
| 94. C33 | AGL(1,ℤ/8) | semidirect |
| 116. C3⋊C8 | C2×C3⋊D3 | semidirect |
| 153. C32 | #908 | semidirect |
| 154. C32 | #949 | semidirect |
| 183. C3 | #63825 | semidirect |
| 184. C3 | #64117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C3×#3828 | 2 |
| C32×#208 | 2 |
| #88797 | 2 |
| #88791 | 2 |
| #64117 | 3 |
| #63825 | 3 |