Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
408 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 1. C22×C3×M16 | C2 | semidirect |
| 3. C2×#830 | C2 | semidirect |
| 4. C2×(C2×D3)⋊C8 | C2 | semidirect |
| 5. #4550 | C2 | semidirect |
| 22. C22×M16 | D3 | semidirect |
| 48. C2×C3×C8 | D4 | semidirect |
| 82. C22×D3 | M16 | semidirect |
| 99. C2×Dic3 | M16 | semidirect |
| 129. C2×C8 | #67 | semidirect |
| 219. C3 | #1870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×M16 | 2 |
| C2×C4×#67 | 2 |
| C2×#830 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| #4550 | 2 |
| #1870 | 3 |