Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
184 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 61 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×Dic24 | C2 | semidirect |
| 2. C2×#800 | C2 | semidirect |
| 4. #4696 | C2 | semidirect |
| 5. C3×C4×C16 | C2 | semidirect |
| 21. C4×C16 | D3 | semidirect |
| 97. C3 | #2249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic24 | 2 |
| C2×#800 | 2 |
| C2×D48 | 2 |
| #4696 | 2 |
| C3×C4×C16 | 2 |
| #2249 | 3 |