Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
276 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 7. C2×C3×C4⋊C4 | C4 | semidirect |
| 12. C3⋊#95 | C4 | semidirect |
| 14. #830 | C4 | semidirect |
| 40. C2×C4⋊C4 | Dic3 | semidirect |
| 177. C3 | #1294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#380 | 2 |
| C2×C3⋊#95 | 2 |
| C2×#830 | 2 |
| #1294 | 3 |