Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
558 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 267 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 |
|---|---|---|
| 4. #69046 | C2 | direct (N × H) |
| 27. C2×C3×C16 | Q8 | semidirect |
| 58. C3×C16 | C2×Q8 | semidirect |
| 67. C2×C16 | Dic6 | semidirect |
| 102. C16 | C2×Dic6 | semidirect |
| 124. C2×C3 | #2254 | semidirect |
| 135. C3 | C2×#2254 | semidirect |
| 136. C2 | #69046 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4682 | 2 |
| C2×C3×C4×C16 | 2 |
| C2×#4505 | 2 |
| #69046 | 2 |
| C2×#2254 | 3 |