Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 188 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. C3×C8×Q8 | C2 | semidirect |
| 2. #5027 | C2 | semidirect |
| 4. #4485 | C2 | semidirect |
| 5. #4458 | C2 | semidirect |
| 20. C8×Q8 | D3 | semidirect |
| 51. C3×Q8 | D8 | semidirect |
| 64. C3×C8 | SD16 | semidirect |
| 94. Q8 | D24 | semidirect |
| 108. C8 | #215 | semidirect |
| 124. C3 | #1668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×Q8 | 2 |
| #5027 | 2 |
| #4695 | 2 |
| #4485 | 2 |
| #4458 | 2 |
| #1668 | 3 |