Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
672 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 154 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×C33×D4 | C2 | semidirect |
| 2. C2×C3×C4⋊(C3⋊D3) | C2 | semidirect |
| 3. C3×#3753 | C2 | direct (N × H) |
| 4. C2×C3×C3⋊(C3⋊C8) | C2 | semidirect |
| 5. C2×#3753 | C3 | direct (N × H) |
| 10. C33×D4 | C22 | semidirect |
| 13. C3×C4⋊(C3⋊D3) | C22 | semidirect |
| 14. C3×C3⋊(C3⋊C8) | C22 | semidirect |
| 16. C2×C32×D4 | D3 | semidirect |
| 17. C2×C32×D4 | C2×C3 | semidirect |
| 18. C2×C4⋊(C3⋊D3) | C2×C3 | semidirect |
| 20. #3753 | C2×C3 | direct (N × H) |
| 21. C2×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 42. C32×D4 | C2×D3 | semidirect |
| 43. C32×D4 | C22×C3 | semidirect |
| 48. C4⋊(C3⋊D3) | C22×C3 | semidirect |
| 51. C3⋊(C3⋊C8) | C22×C3 | semidirect |
| 54. C2×C33 | D8 | semidirect |
| 59. C2×C3×D4 | C3×D3 | semidirect |
| 60. C2×C3×D4 | C3⋊D3 | semidirect |
| 86. C33 | C2×D8 | semidirect |
| 98. C3×D4 | C2×C3×D3 | semidirect |
| 99. C3×D4 | C2×C3⋊D3 | semidirect |
| 112. C2×C32 | #213 | semidirect |
| 113. C2×C32 | C3×D8 | semidirect |
| 119. C2×D4 | C3×C3⋊D3 | semidirect |
| 142. C32 | C2×#213 | semidirect |
| 143. C32 | C2×C3×D8 | semidirect |
| 149. D4 | C2×C3×C3⋊D3 | semidirect |
| 158. C2×C3 | C3×#213 | semidirect |
| 159. C2×C3 | #3753 | direct (N × H) |
| 171. C3 | C2×C3×#213 | semidirect |
| 172. C3 | C2×#3753 | direct (N × H) |
| 175. C2 | C3×#3753 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D4 | 2 |
| C2×C3×C4⋊(C3⋊D3) | 2 |
| C3×#3753 | 2 |
| C2×C3×C3⋊(C3⋊C8) | 2 |
| C2×#3753 | 3 |
| C2×C3×#213 | 3 |