Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2410 conjugacy classes of subgroups.
The subgroup lattice has 368 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #71593 | C2 | semidirect |
| 5. C2×#4527 | C2 | semidirect |
| 9. C3×#518 | C4 | semidirect |
| 18. #5798 | C4 | semidirect |
| 20. C2×D4×Dic3 | C4 | semidirect |
| 40. C23×Dic3 | C2×C4 | semidirect |
| 43. C3×#117 | C2×C4 | semidirect |
| 47. C2×C3×C22⋊C4 | C2×C4 | semidirect |
| 54. C2×#217 | C2×C4 | semidirect |
| 55. C2×#217 | C2×C4 | semidirect |
| 63. #926 | C2×C4 | semidirect |
| 65. C2×C4⋊Dic3 | C2×C4 | semidirect |
| 67. C2×C4×Dic3 | C2×C4 | semidirect |
| 74. #518 | Dic3 | semidirect |
| 152. #117 | C2×Dic3 | semidirect |
| 166. C2×C22⋊C4 | C2×Dic3 | semidirect |
| 357. C3 | #20354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#518 | 2 |
| C2×#5798 | 2 |
| #71593 | 2 |
| C2×#4527 | 2 |
| #20354 | 3 |