Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
110 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 2. C3×C4×C16 | C2 | semidirect |
| 3. #4458 | C2 | semidirect |
| 13. C4×C16 | D3 | semidirect |
| 24. D24 | C8 | semidirect |
| 94. C3 | #1331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D24 | 2 |
| C3×C4×C16 | 2 |
| #4458 | 2 |
| #1331 | 3 |