Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
532 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#4909 | C2 | semidirect |
| 2. C2×#4896 | C2 | semidirect |
| 4. C2×#4515 | C2 | semidirect |
| 5. C2×#4497 | C2 | semidirect |
| 6. C2×#4492 | C2 | semidirect |
| 7. C3×#1387 | C2 | semidirect |
| 38. #1387 | D3 | semidirect |
| 56. C2×Dic12 | D4 | semidirect |
| 75. C3×M32 | D4 | semidirect |
| 78. C3×#108 | D4 | semidirect |
| 211. M32 | D12 | semidirect |
| 217. #108 | D12 | semidirect |
| 415. C3 | #13308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4909 | 2 |
| C2×#4896 | 2 |
| #79150 | 2 |
| C2×#4515 | 2 |
| C2×#4497 | 2 |
| C2×#4492 | 2 |
| C3×#1387 | 2 |
| #13308 | 3 |