Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
232 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 5. C2×C3×C4⋊C4 | C4 | semidirect |
| 7. C2×C3×C42 | C4 | semidirect |
| 10. #834 | C4 | semidirect |
| 29. C2×C4⋊C4 | Dic3 | semidirect |
| 32. C2×C42 | Dic3 | semidirect |
| 135. C3 | #1393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#390 | 2 |
| C2×#834 | 2 |
| #1393 | 3 |