Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
464 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 73 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. D4×C3⋊#157 | C2 | semidirect |
| 3. #11723107 | C2 | semidirect |
| 4. #11723094 | C2 | semidirect |
| 5. C8×C3⋊#157 | C2 | semidirect |
| 13. C33×D8 | C4 | semidirect |
| 14. C3×#3753 | C4 | semidirect |
| 15. C3×#3745 | C4 | semidirect |
| 28. C33×D4 | C2×C4 | semidirect |
| 30. C3×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 33. C33×C8 | C2×C4 | semidirect |
| 34. C3×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 45. C32×D8 | Dic3 | semidirect |
| 46. #3753 | Dic3 | semidirect |
| 47. #3745 | Dic3 | semidirect |
| 59. C3⋊#157 | D8 | direct (N × H) |
| 76. C32×D4 | C2×Dic3 | semidirect |
| 78. C4⋊(C3⋊D3) | C2×Dic3 | semidirect |
| 86. C32×C8 | C2×Dic3 | semidirect |
| 87. C3⋊(C3⋊C8) | C2×Dic3 | semidirect |
| 102. C3×D8 | #157 | semidirect |
| 135. C33 | C4×D8 | semidirect |
| 142. C3×D4 | C2×#157 | semidirect |
| 154. C3×C8 | C2×#157 | semidirect |
| 173. D8 | C3⋊#157 | direct (N × H) |
| 200. C32 | Dic3×D8 | semidirect |
| 204. D4 | C2×C3⋊#157 | semidirect |
| 212. C8 | C2×C3⋊#157 | semidirect |
| 237. C3 | D8×#157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C3⋊#157 | 2 |
| C3×D8×C3⋊D3 | 2 |
| #11723107 | 2 |
| #11723094 | 2 |
| C8×C3⋊#157 | 2 |
| D8×#157 | 3 |
| Dic3×D8 | 9 |