Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1880 conjugacy classes of subgroups; only the 901 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 901 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. C22×Dic3⋊C4 | C2 | semidirect |
| 5. C22×C4×Dic3 | C2 | semidirect |
| 6. C2×#877 | C2 | direct (N × H) |
| 10. C23×Dic3 | C4 | semidirect |
| 17. C2×Dic3⋊C4 | C22 | semidirect |
| 18. C2×C4×Dic3 | C22 | semidirect |
| 19. #877 | C22 | direct (N × H) |
| 35. C22×Dic3 | C2×C4 | semidirect |
| 42. Dic3⋊C4 | C23 | semidirect |
| 43. C4×Dic3 | C23 | semidirect |
| 68. C2×Dic3 | C22×C4 | semidirect |
| 92. C22×C3 | #117 | semidirect |
| 118. C2×C3 | C2×#117 | semidirect |
| 123. C22 | #877 | direct (N × H) |
| 132. C3 | C22×#117 | semidirect |
| 134. C2 | C2×#877 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic3 | 2 |
| C22×C3×C22⋊C4 | 2 |
| C22×#217 | 2 |
| C22×Dic3⋊C4 | 2 |
| C22×C4×Dic3 | 2 |
| C2×#877 | 2 |
| C22×#117 | 3 |