Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
347 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 347 conjugacy classes of subgroups — too many to draw. Only its 70 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. #5426 | C2 | direct (N × H) |
| 3. C2×#859 | C2 | semidirect |
| 5. C2×#41⋊C3 | C4 | semidirect |
| 9. #859 | C22 | semidirect |
| 19. #41⋊C3 | C2×C4 | semidirect |
| 20. C2×SL(2,𝔽3) | C2×C4 | semidirect |
| 25. C2×#41 | Dic3 | semidirect |
| 46. SL(2,𝔽3) | C22×C4 | semidirect |
| 51. #41 | C2×Dic3 | semidirect |
| 125. C2 | #5426 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#41⋊C3 | 2 |
| #5426 | 2 |
| C2×#859 | 2 |
| C2×#417 | 3 |
| C2×C4⋊Dic3 | 4 |