Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
912 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 113 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. #83169 | C2 | semidirect |
| 3. #71759 | C2 | semidirect |
| 4. #69396 | C2 | semidirect |
| 5. #67611 | C2 | semidirect |
| 44. #869 | D4 | semidirect |
| 49. C4⋊(C3⋊C8) | D4 | semidirect |
| 83. C3×C42 | SD16 | semidirect |
| 176. C42 | #214 | semidirect |
| 238. C3 | #10290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2867 | 2 |
| #83169 | 2 |
| #71759 | 2 |
| #69396 | 2 |
| #67611 | 2 |
| #10290 | 3 |