Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
566 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 139 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. C3×C4×#108 | C2 | semidirect |
| 3. C2×#4495 | C2 | semidirect |
| 4. #69743 | C2 | semidirect |
| 21. C4×#108 | D3 | semidirect |
| 38. C3×#108 | D4 | semidirect |
| 102. #108 | D12 | semidirect |
| 162. C3×C4 | #361 | semidirect |
| 198. C4 | #4495 | semidirect |
| 202. C3 | #13257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4695 | 2 |
| C3×C4×#108 | 2 |
| C2×#4495 | 2 |
| #69743 | 2 |
| #13257 | 3 |