Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
328 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 63 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×C3⋊#157 | C2 | semidirect |
| 3. #88994 | C2 | semidirect |
| 4. C4⋊(C3⋊#157) | C2 | semidirect |
| 5. C4×C3⋊#157 | C2 | semidirect |
| 12. C33×D4 | C4 | semidirect |
| 13. C3×#638 | C4 | semidirect |
| 14. C3×C4⋊(C3⋊D3) | C4 | semidirect |
| 22. C22×C33 | C2×C4 | semidirect |
| 25. C2×C3×C3⋊D3 | C2×C4 | semidirect |
| 29. C3⋊#157 | D4 | direct (N × H) |
| 30. C33×C4 | C2×C4 | semidirect |
| 31. C3×C3⋊Dic3 | C2×C4 | semidirect |
| 41. C32×D4 | Dic3 | semidirect |
| 42. #638 | Dic3 | semidirect |
| 43. C4⋊(C3⋊D3) | Dic3 | semidirect |
| 61. C22×C32 | C2×Dic3 | semidirect |
| 64. C2×C3⋊D3 | C2×Dic3 | semidirect |
| 75. C32×C4 | C2×Dic3 | semidirect |
| 76. C3⋊Dic3 | C2×Dic3 | semidirect |
| 79. C33 | C4×D4 | semidirect |
| 86. C3×D4 | #157 | semidirect |
| 118. C22×C3 | C2×#157 | semidirect |
| 126. C3×C4 | C2×#157 | semidirect |
| 133. C32 | D4×Dic3 | semidirect |
| 137. D4 | C3⋊#157 | direct (N × H) |
| 159. C22 | C2×C3⋊#157 | semidirect |
| 164. C4 | C2×C3⋊#157 | semidirect |
| 167. C3 | D4×#157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊#157 | 2 |
| C3×D4×C3⋊D3 | 2 |
| #88994 | 2 |
| C4⋊(C3⋊#157) | 2 |
| C4×C3⋊#157 | 2 |
| D4×#157 | 3 |
| D4×Dic3 | 9 |