Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
550 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 125 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. #2971⋊C3 | C2 | direct (N × H) |
| 3. C2×C8×SL(2,𝔽3) | C2 | semidirect |
| 4. C2×#2971 | C3 | semidirect |
| 11. C8×SL(2,𝔽3) | C22 | semidirect |
| 14. #2971 | C2×C3 | semidirect |
| 57. C2×SL(2,𝔽3) | M16 | semidirect |
| 118. SL(2,𝔽3) | C2×M16 | semidirect |
| 152. C2×C8 | #41⋊C3 | semidirect |
| 215. C8 | C2×#41⋊C3 | semidirect |
| 240. C2 | #2971⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#41⋊C3 | 2 |
| #2971⋊C3 | 2 |
| C2×C8×SL(2,𝔽3) | 2 |
| C2×#2971 | 3 |
| C2×C3×#97 | 4 |