Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 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. #83805 | C2 | semidirect |
| 2. #83799 | C2 | semidirect |
| 3. C2×#4908 | C2 | semidirect |
| 4. C3×#2117 | C2 | semidirect |
| 5. #71450 | C2 | semidirect |
| 6. C2×#4516 | C2 | semidirect |
| 7. #67822 | C2 | semidirect |
| 37. #2117 | D3 | semidirect |
| 61. C2×Dic12 | D4 | semidirect |
| 72. C2×D24 | D4 | semidirect |
| 77. C3×M32 | D4 | semidirect |
| 84. #819 | D4 | semidirect |
| 213. M32 | #67 | semidirect |
| 415. C3 | #13310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83805 | 2 |
| #83799 | 2 |
| C2×#4908 | 2 |
| C3×#2117 | 2 |
| #71450 | 2 |
| C2×#4516 | 2 |
| #67822 | 2 |
| #13310 | 3 |