Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
544 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 544 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×#946 | C2 | semidirect |
| 2. C22×#215 | C2 | semidirect |
| 3. C22×ΓL(1,𝔽25) | C2 | semidirect |
| 5. C2×C3×#103 | C2 | semidirect |
| 6. C2×#821 | C2 | semidirect |
| 7. C2×#807 | C2 | semidirect |
| 8. #4812 | C2 | direct (N × H) |
| 17. #946 | C22 | semidirect |
| 19. C2×#215 | C22 | semidirect |
| 26. C2×ΓL(1,𝔽25) | C22 | semidirect |
| 29. C3×#103 | C22 | semidirect |
| 30. #821 | C22 | semidirect |
| 31. #807 | C22 | semidirect |
| 38. C2×#103 | D3 | semidirect |
| 71. C2×C3⋊C8 | D4 | semidirect |
| 94. #103 | C2×D3 | semidirect |
| 128. C3⋊C8 | C2×D4 | semidirect |
| 215. C2×C3 | #468 | semidirect |
| 240. C3 | C2×#468 | semidirect |
| 243. C2 | #4812 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#946 | 2 |
| C22×#215 | 2 |
| C22×ΓL(1,𝔽25) | 2 |
| C2×#895 | 2 |
| C2×C3×#103 | 2 |
| C2×#821 | 2 |
| C2×#807 | 2 |
| #4812 | 2 |
| C2×#468 | 3 |