Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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. #79116 | C2 | semidirect |
| 3. #71450 | C2 | semidirect |
| 4. #71438 | C2 | semidirect |
| 5. C2×#4488 | C2 | semidirect |
| 6. C3×#1383 | C2 | semidirect |
| 7. #67735 | C2 | semidirect |
| 21. #4897 | C4 | semidirect |
| 22. #4896 | C4 | semidirect |
| 36. #1383 | D3 | semidirect |
| 49. C2×Dic12 | C2×C4 | semidirect |
| 55. C2×D24 | C2×C4 | semidirect |
| 71. C3×#108 | C2×C4 | semidirect |
| 198. #108 | C4×D3 | semidirect |
| 380. C3 | #13005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79256 | 2 |
| #79116 | 2 |
| #71450 | 2 |
| #71438 | 2 |
| C2×#4488 | 2 |
| C3×#1383 | 2 |
| #67735 | 2 |
| #13005 | 3 |