Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
912 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 109 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. C3×#3208 | C2 | semidirect |
| 2. #83355 | C2 | semidirect |
| 4. #71839 | C2 | semidirect |
| 5. #71759 | C2 | semidirect |
| 6. #70774 | C2 | semidirect |
| 7. #67736 | C2 | semidirect |
| 31. #3208 | D3 | semidirect |
| 45. C3×C4⋊Q8 | D4 | semidirect |
| 46. C3×C4⋊Q8 | D4 | semidirect |
| 71. C3×C4⋊C8 | D4 | semidirect |
| 79. C4⋊(C3⋊C8) | D4 | semidirect |
| 151. C4×Dic3 | SD16 | semidirect |
| 165. C4⋊Q8 | #67 | semidirect |
| 166. C4⋊Q8 | #67 | semidirect |
| 192. C4⋊C8 | #67 | semidirect |
| 390. C3 | #10290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3208 | 2 |
| #83355 | 2 |
| #83185 | 2 |
| #71839 | 2 |
| #71759 | 2 |
| #70774 | 2 |
| #67736 | 2 |
| #10290 | 3 |