Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
186 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 55 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×#493 | C2 | semidirect |
| 2. C2×#826 | C2 | semidirect |
| 3. C4×D24 | C2 | semidirect |
| 4. #4562 | C2 | semidirect |
| 5. C4⋊(C3⋊C16) | C2 | semidirect |
| 18. #493 | D3 | semidirect |
| 36. D24 | D4 | semidirect |
| 88. C3×C4 | D16 | semidirect |
| 122. C4 | #826 | semidirect |
| 125. C3 | #2206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#493 | 2 |
| C2×#826 | 2 |
| C4×D24 | 2 |
| #4562 | 2 |
| C4⋊(C3⋊C16) | 2 |
| #2206 | 3 |