Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
152 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 85 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. #4487 | C2 | direct (N × H) |
| 13. #812 | C4 | semidirect |
| 15. C2×C3⋊C16 | C4 | semidirect |
| 33. C3⋊C16 | C2×C4 | semidirect |
| 97. C2×C3 | #365 | semidirect |
| 108. C3 | C2×#365 | semidirect |
| 111. C2 | #4487 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#106 | 2 |
| C2×#819 | 2 |
| C2×#812 | 2 |
| #4487 | 2 |
| C2×#365 | 3 |