Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
340 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 79 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. #5745 | C2 | semidirect |
| 3. #5132 | C2 | semidirect |
| 4. C2×#823 | C2 | semidirect |
| 5. C2×#823 | C2 | semidirect |
| 6. C3×#344 | C2 | semidirect |
| 7. #4533 | C2 | semidirect |
| 33. #344 | D3 | semidirect |
| 54. C3×M16 | D4 | semidirect |
| 64. #208 | D4 | semidirect |
| 143. M16 | D12 | semidirect |
| 222. C3 | #1914 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5745 | 2 |
| #5525 | 2 |
| #5132 | 2 |
| C2×#823 | 2 |
| C3×#344 | 2 |
| #4533 | 2 |
| #1914 | 3 |