Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1230 conjugacy classes of subgroups; only the 651 normal subgroups are shown.
This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 651 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 |
|---|---|---|
| 3. #69439 | C2 | direct (N × H) |
| 100. C2×C3 | #1843 | semidirect |
| 111. C3 | C2×#1843 | semidirect |
| 112. C2 | #69439 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#376 | 2 |
| C22×C4⋊(C3⋊C8) | 2 |
| #69439 | 2 |
| C2×#1843 | 3 |