Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1008 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 229 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×ΓL(1,𝔽25) | C2 | semidirect |
| 3. C2×#892 | C2 | semidirect |
| 4. C2×C3×#102 | C2 | semidirect |
| 5. C2×#832 | C2 | semidirect |
| 6. C2×#821 | C2 | semidirect |
| 7. C2×#809 | C2 | semidirect |
| 8. #4770 | C2 | direct (N × H) |
| 15. C2×D3×D4 | C4 | semidirect |
| 19. C22×C3×C8 | C22 | semidirect |
| 20. C2×C3×C4⋊C4 | C22 | semidirect |
| 22. C2×C4⋊Dic3 | C22 | semidirect |
| 24. C22×C3⋊C8 | C22 | semidirect |
| 26. C2×ΓL(1,𝔽25) | C22 | semidirect |
| 28. #892 | C22 | semidirect |
| 29. C3×#102 | C22 | semidirect |
| 30. #832 | C22 | semidirect |
| 31. #821 | C22 | semidirect |
| 32. #809 | C22 | semidirect |
| 40. C2×#102 | D3 | semidirect |
| 60. D3×D4 | C2×C4 | semidirect |
| 70. C2×C3×C8 | C23 | semidirect |
| 72. C3×C4⋊C4 | C23 | semidirect |
| 75. C4⋊Dic3 | C23 | semidirect |
| 78. C2×C3⋊C8 | C23 | semidirect |
| 92. C22×C8 | C2×D3 | semidirect |
| 96. C2×C4⋊C4 | C2×D3 | semidirect |
| 102. #102 | C2×D3 | semidirect |
| 174. C2×C8 | C22×D3 | semidirect |
| 178. C4⋊C4 | C22×D3 | semidirect |
| 244. C2×C3 | #418 | semidirect |
| 273. C3 | C2×#418 | semidirect |
| 277. C2 | #4770 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×D4 | 2 |
| C22×ΓL(1,𝔽25) | 2 |
| C2×#892 | 2 |
| C2×C3×#102 | 2 |
| C2×#832 | 2 |
| C2×#821 | 2 |
| C2×#809 | 2 |
| #4770 | 2 |
| C2×#418 | 3 |