Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
388 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 195 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 |
|---|---|---|
| 2. C3×C8×Q8 | C2 | semidirect |
| 3. Q8×C3⋊C8 | C2 | semidirect |
| 5. #4831 | C2 | semidirect |
| 7. #4679 | C2 | semidirect |
| 29. C8×Q8 | D3 | semidirect |
| 50. ΓL(1,𝔽25) | Q8 | direct (N × H) |
| 68. C3×Q8 | M16 | semidirect |
| 81. C3×C8 | C2×Q8 | semidirect |
| 83. C3⋊C8 | C2×Q8 | semidirect |
| 116. Q8 | ΓL(1,𝔽25) | direct (N × H) |
| 130. C8 | D3×Q8 | semidirect |
| 146. C3 | Q8×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D3×Q8 | 2 |
| C3×C8×Q8 | 2 |
| Q8×C3⋊C8 | 2 |
| #4837 | 2 |
| #4831 | 2 |
| C4×ΓL(1,𝔽25) | 2 |
| #4679 | 2 |
| Q8×M16 | 3 |