Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
224 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 125 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×C82 | C2 | semidirect |
| 5. #4455 | C2 | semidirect |
| 6. #4454 | C2 | semidirect |
| 7. C8×C3⋊C8 | C2 | semidirect |
| 28. C82 | D3 | semidirect |
| 42. ΓL(1,𝔽25) | C8 | direct (N × H) |
| 68. C3×C8 | C2×C8 | semidirect |
| 69. C3×C8 | M16 | semidirect |
| 72. C3⋊C8 | C2×C8 | semidirect |
| 112. C8 | D3×C8 | semidirect |
| 113. C8 | ΓL(1,𝔽25) | direct (N × H) |
| 128. C3 | C8×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×ΓL(1,𝔽25) | 2 |
| #4685 | 2 |
| C4×D3×C8 | 2 |
| C3×C82 | 2 |
| #4455 | 2 |
| #4454 | 2 |
| C8×C3⋊C8 | 2 |
| C8×M16 | 3 |