Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
387 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 387 conjugacy classes of subgroups — too many to draw. Only its 79 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. #73010 | C2 | direct (N × H) |
| 152. C2×C8 | #226 | semidirect |
| 204. C8 | C2×#226 | semidirect |
| 224. C2 | #73010 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#226 | 2 |
| C2×C8×SL(2,𝔽3) | 2 |
| C2×SL(2,𝔽3)⋊C8 | 2 |
| #73010 | 2 |
| C2×#1584 | 3 |
| C2×#815 | 4 |