Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
252 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 4. C3×Q8⋊C8 | C2 | semidirect |
| 5. #4535 | C2 | semidirect |
| 6. #4484 | C2 | semidirect |
| 7. #4456 | C2 | semidirect |
| 34. Q8⋊C8 | D3 | semidirect |
| 86. C3×Q8 | M16 | semidirect |
| 106. Dic6 | M16 | semidirect |
| 162. Q8 | ΓL(1,𝔽25) | semidirect |
| 204. C3 | #1491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D3×Q8 | 2 |
| #4835 | 2 |
| C4×ΓL(1,𝔽25) | 2 |
| C3×Q8⋊C8 | 2 |
| #4535 | 2 |
| #4484 | 2 |
| #4456 | 2 |
| #1491 | 3 |