Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
532 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 97 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×#3060 | C2 | semidirect |
| 2. #83894 | C2 | semidirect |
| 3. #83805 | C2 | semidirect |
| 4. #72080 | C2 | semidirect |
| 5. #72006 | C2 | semidirect |
| 6. C2×#4488 | C2 | semidirect |
| 7. #67720 | C2 | semidirect |
| 36. #3060 | D3 | semidirect |
| 71. C2×Dic12 | D4 | semidirect |
| 76. C2×D24 | D4 | semidirect |
| 89. #819 | D4 | semidirect |
| 95. C2×C3⋊C16 | D4 | semidirect |
| 445. C3 | #13318 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3060 | 2 |
| #83894 | 2 |
| #83805 | 2 |
| #72080 | 2 |
| #72006 | 2 |
| C2×#4488 | 2 |
| #67720 | 2 |
| #13318 | 3 |