Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1504 conjugacy classes of subgroups; only the 821 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 821 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. C22×C3×M16 | C2 | semidirect |
| 3. C23×C3⋊C8 | C2 | semidirect |
| 4. C2×#907 | C2 | direct (N × H) |
| 5. C22×ΓL(1,𝔽25) | C2 | semidirect |
| 6. C22×D3×C8 | C2 | semidirect |
| 15. C2×C3×M16 | C22 | semidirect |
| 19. C22×C3⋊C8 | C22 | semidirect |
| 20. #907 | C22 | direct (N × H) |
| 21. C2×ΓL(1,𝔽25) | C22 | semidirect |
| 22. C2×D3×C8 | C22 | semidirect |
| 26. C22×M16 | D3 | semidirect |
| 43. C3×M16 | C23 | semidirect |
| 47. C2×C3⋊C8 | C23 | semidirect |
| 48. ΓL(1,𝔽25) | C23 | semidirect |
| 49. D3×C8 | C23 | semidirect |
| 59. C2×M16 | C2×D3 | semidirect |
| 99. M16 | C22×D3 | semidirect |
| 106. C22×C3 | #131 | semidirect |
| 135. C2×C3 | C2×#131 | semidirect |
| 141. C22 | #907 | direct (N × H) |
| 148. C3 | C22×#131 | semidirect |
| 151. C2 | C2×#907 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#235 | 2 |
| C22×C3×M16 | 2 |
| C23×C3⋊C8 | 2 |
| C2×#907 | 2 |
| C22×ΓL(1,𝔽25) | 2 |
| C22×D3×C8 | 2 |
| C22×#131 | 3 |