Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
146 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 65 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. #4901 | C2 | semidirect |
| 3. C3×C4×C16 | C2 | semidirect |
| 4. #4508 | C2 | semidirect |
| 5. #4463 | C2 | semidirect |
| 21. C4×C16 | D3 | semidirect |
| 97. C3 | #2170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4901 | 2 |
| #4700 | 2 |
| C3×C4×C16 | 2 |
| #4508 | 2 |
| #4463 | 2 |
| #2170 | 3 |