Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
454 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 91 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×#2143 | C2 | semidirect |
| 3. #72081 | C2 | semidirect |
| 4. C2×#4516 | C2 | semidirect |
| 5. #70707 | C2 | semidirect |
| 6. C2×#4495 | C2 | semidirect |
| 7. #67814 | C2 | semidirect |
| 32. #2143 | D3 | semidirect |
| 67. C3×#108 | D4 | semidirect |
| 183. #108 | #67 | semidirect |
| 342. C3 | #13417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83906 | 2 |
| C3×#2143 | 2 |
| #72081 | 2 |
| C2×#4516 | 2 |
| #70707 | 2 |
| C2×#4495 | 2 |
| #67814 | 2 |
| #13417 | 3 |