Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1014 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1014 conjugacy classes of subgroups — too many to draw. Only its 267 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. #83823 | C2 | semidirect |
| 3. #72041 | C2 | semidirect |
| 4. #71763 | C2 | semidirect |
| 5. #69779 | C2 | semidirect |
| 10. C3×#493 | C4 | semidirect |
| 30. C2×C3×D8 | C2×C4 | semidirect |
| 33. C3×#127 | C2×C4 | semidirect |
| 39. C3×C4×C8 | C2×C4 | semidirect |
| 43. #818 | D4 | semidirect |
| 44. #817 | D4 | semidirect |
| 50. #493 | Dic3 | semidirect |
| 90. C2×D8 | C2×Dic3 | semidirect |
| 94. #127 | C2×Dic3 | semidirect |
| 106. C4×C8 | C2×Dic3 | semidirect |
| 199. C3 | #23201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#493 | 2 |
| #83823 | 2 |
| #72041 | 2 |
| #71763 | 2 |
| #69779 | 2 |
| #23201 | 3 |