Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 172 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 |
| 3. #5020 | C2 | semidirect |
| 6. #4482 | C2 | semidirect |
| 7. #4457 | C2 | semidirect |
| 27. C8×Q8 | D3 | semidirect |
| 67. C3×Q8 | SD16 | semidirect |
| 83. C3×C8 | SD16 | semidirect |
| 121. Q8 | #204 | semidirect |
| 137. C8 | #215 | semidirect |
| 154. C3 | #1666 | 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 |
| #5020 | 2 |
| #4693 | 2 |
| #4485 | 2 |
| #4482 | 2 |
| #4457 | 2 |
| #1666 | 3 |