Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 148 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 |
|---|---|---|
| 1. C2×C3×D16 | C2 | semidirect |
| 2. #5160 | C2 | semidirect |
| 3. #4901 | C2 | semidirect |
| 4. #4563 | C2 | semidirect |
| 5. #4506 | C2 | semidirect |
| 18. C2×D16 | D3 | semidirect |
| 104. C3 | #2221 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D16 | 2 |
| #5160 | 2 |
| #4901 | 2 |
| #4563 | 2 |
| #4506 | 2 |
| #2221 | 3 |