Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
698 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 119 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×#5151 | C2 | semidirect |
| 2. C22×#826 | C2 | semidirect |
| 3. C22×D48 | C2 | semidirect |
| 4. C2×C3×#357 | C2 | semidirect |
| 5. #70628 | C2 | semidirect |
| 6. C2×#4491 | C2 | semidirect |
| 7. #67804 | C2 | semidirect |
| 34. C2×#357 | D3 | semidirect |
| 68. C2×D24 | D4 | semidirect |
| 71. C2×C3×C16 | D4 | semidirect |
| 79. C2×C3⋊C16 | D4 | semidirect |
| 198. C2×C16 | #67 | semidirect |
| 235. C2×Dic3 | D16 | semidirect |
| 410. C3 | #13325 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5151 | 2 |
| C22×#826 | 2 |
| C22×D48 | 2 |
| C2×C3×#357 | 2 |
| #70628 | 2 |
| C2×#4491 | 2 |
| #67804 | 2 |
| #13325 | 3 |