Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. C2×#938 | C2 | semidirect |
| 2. C22×#213 | C2 | semidirect |
| 3. C22×ΓL(1,𝔽25) | C2 | semidirect |
| 4. C2×#895 | C2 | semidirect |
| 5. C2×C3×#102 | C2 | semidirect |
| 6. C2×#821 | C2 | semidirect |
| 7. C2×#808 | C2 | semidirect |
| 8. #4782 | C2 | direct (N × H) |
| 19. #938 | C22 | semidirect |
| 21. C2×#213 | C22 | semidirect |
| 26. C2×ΓL(1,𝔽25) | C22 | semidirect |
| 28. #895 | C22 | semidirect |
| 29. C3×#102 | C22 | semidirect |
| 30. #821 | C22 | semidirect |
| 31. #808 | C22 | semidirect |
| 39. C2×#102 | D3 | semidirect |
| 72. C2×C3⋊C8 | D4 | semidirect |
| 96. #102 | C2×D3 | semidirect |
| 132. C3⋊C8 | C2×D4 | semidirect |
| 227. C2×C3 | #469 | semidirect |
| 255. C3 | C2×#469 | semidirect |
| 259. C2 | #4782 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#938 | 2 |
| C22×#213 | 2 |
| C22×ΓL(1,𝔽25) | 2 |
| C2×#895 | 2 |
| C2×C3×#102 | 2 |
| C2×#821 | 2 |
| C2×#808 | 2 |
| #4782 | 2 |
| C2×#469 | 3 |