Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
336 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 101 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. #4452 | C2 | direct (N × H) |
| 8. C22×Dic6 | C4 | semidirect |
| 10. C2×C4⋊Dic3 | C4 | semidirect |
| 13. #924 | C4 | semidirect |
| 41. C2×Dic6 | C2×C4 | semidirect |
| 45. C4⋊Dic3 | C2×C4 | semidirect |
| 169. C2×C3 | #328 | semidirect |
| 193. C3 | C2×#328 | semidirect |
| 197. C2 | #4452 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#924 | 2 |
| C2×C3×#95 | 2 |
| C2×#830 | 2 |
| #4452 | 2 |
| C2×#328 | 3 |