Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1320 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 565 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×C4⋊Dic3 | C2 | semidirect |
| 5. C22×Dic3⋊C4 | C2 | semidirect |
| 6. C22×Dic3⋊C4 | C2 | semidirect |
| 7. C22×C4×Dic3 | C2 | semidirect |
| 8. C2×#879 | C2 | direct (N × H) |
| 20. C2×C4⋊Dic3 | C22 | semidirect |
| 21. C2×Dic3⋊C4 | C22 | semidirect |
| 22. C2×Dic3⋊C4 | C22 | semidirect |
| 23. C2×C4×Dic3 | C22 | semidirect |
| 24. #879 | C22 | direct (N × H) |
| 53. C4⋊Dic3 | C23 | semidirect |
| 54. Dic3⋊C4 | C23 | semidirect |
| 55. Dic3⋊C4 | C23 | semidirect |
| 56. C4×Dic3 | C23 | semidirect |
| 121. C22×C3 | #126 | semidirect |
| 154. C2×C3 | C2×#126 | semidirect |
| 162. C22 | #879 | direct (N × H) |
| 173. C3 | C22×#126 | semidirect |
| 175. C2 | C2×#879 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C22⋊C4 | 2 |
| C22×#217 | 2 |
| C22×C4⋊Dic3 | 2 |
| C22×Dic3⋊C4 | 2 |
| C22×C4×Dic3 | 2 |
| C2×#879 | 2 |
| C22×#126 | 3 |