Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
656 conjugacy classes of subgroups; only the 357 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 357 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 |
|---|---|---|
| 3. C2×C3×C4×C8 | C2 | semidirect |
| 4. C2×#815 | C2 | semidirect |
| 5. C2×C4×C3⋊C8 | C2 | semidirect |
| 6. C4×ΓL(1,𝔽25) | C2 | direct (N × H) |
| 15. C2×ΓL(1,𝔽25) | C4 | direct (N × H) |
| 19. C3×C4×C8 | C22 | semidirect |
| 20. #815 | C22 | semidirect |
| 21. C4×C3⋊C8 | C22 | semidirect |
| 27. C2×C4×C8 | D3 | semidirect |
| 38. C2×C3×C8 | C2×C4 | semidirect |
| 45. C2×C3⋊C8 | C2×C4 | semidirect |
| 47. ΓL(1,𝔽25) | C2×C4 | direct (N × H) |
| 61. C4×C8 | C2×D3 | semidirect |
| 66. C2×C3×C4 | M16 | semidirect |
| 78. C3×C8 | C22×C4 | semidirect |
| 79. C3⋊C8 | C22×C4 | semidirect |
| 93. C2×C8 | C4×D3 | semidirect |
| 107. C3×C4 | C2×M16 | semidirect |
| 122. C2×C4 | ΓL(1,𝔽25) | direct (N × H) |
| 128. C8 | C2×C4×D3 | semidirect |
| 129. C2×C3 | C4×M16 | semidirect |
| 142. C4 | C2×ΓL(1,𝔽25) | direct (N × H) |
| 144. C3 | C2×C4×M16 | semidirect |
| 146. C2 | C4×ΓL(1,𝔽25) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×ΓL(1,𝔽25) | 2 |
| C2×C42×D3 | 2 |
| C2×C3×C4×C8 | 2 |
| C2×#815 | 2 |
| C2×C4×C3⋊C8 | 2 |
| C4×ΓL(1,𝔽25) | 2 |
| C2×C4×M16 | 3 |