Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
158 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 53 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. C3×C4×Q16 | C2 | semidirect |
| 2. C2×#829 | C2 | semidirect |
| 5. #4492 | C2 | semidirect |
| 7. C4⋊(C3⋊C16) | C2 | semidirect |
| 25. C4×Q16 | D3 | semidirect |
| 140. C3 | #2211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×Q16 | 2 |
| C2×#829 | 2 |
| C2×#828 | 2 |
| #4696 | 2 |
| #4492 | 2 |
| #4491 | 2 |
| C4⋊(C3⋊C16) | 2 |
| #2211 | 3 |