Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
712 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 389 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. #4936 | C2 | direct (N × H) |
| 9. C2×C3×C42 | C4 | semidirect |
| 29. C3×C42 | C2×C4 | semidirect |
| 36. C2×C42 | Dic3 | semidirect |
| 66. C42 | C2×Dic3 | semidirect |
| 93. C2×C3 | #382 | semidirect |
| 109. C3 | C2×#382 | semidirect |
| 110. C2 | #4936 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C42 | 2 |
| C22×C4⋊Dic3 | 2 |
| C2×C3⋊#95 | 2 |
| #4936 | 2 |
| C2×#382 | 3 |