Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
448 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. C2×C3×H(3,ℤ/4) | C2 | semidirect |
| 3. C2×#4553 | C2 | semidirect |
| 4. #67482 | C2 | semidirect |
| 5. #67481 | C2 | semidirect |
| 10. C2×#904 | C4 | semidirect |
| 11. #5137 | C4 | semidirect |
| 13. #5135 | C4 | semidirect |
| 18. #5106 | C4 | semidirect |
| 26. C2×H(3,ℤ/4) | D3 | semidirect |
| 55. C2×Dic12 | C2×C4 | semidirect |
| 58. C2×D24 | C2×C4 | semidirect |
| 63. #817 | C2×C4 | semidirect |
| 64. #817 | C2×C4 | semidirect |
| 377. C3 | #11685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83771 | 2 |
| C2×C3×H(3,ℤ/4) | 2 |
| C2×#4553 | 2 |
| #67482 | 2 |
| #67481 | 2 |
| #11685 | 3 |