Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1464 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 525 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. C22×D3×Q8 | C2 | semidirect |
| 3. C22×C3×SD16 | C2 | semidirect |
| 4. C22×#216 | C2 | semidirect |
| 5. C22×#214 | C2 | semidirect |
| 6. C2×#915 | C2 | direct (N × H) |
| 7. C22×Dic12 | C2 | semidirect |
| 8. C22×ΓL(1,𝔽25) | C2 | semidirect |
| 15. C2×D3×Q8 | C22 | semidirect |
| 23. C2×C3×SD16 | C22 | semidirect |
| 25. C2×#216 | C22 | semidirect |
| 26. C2×#214 | C22 | semidirect |
| 28. #915 | C22 | direct (N × H) |
| 29. C2×Dic12 | C22 | semidirect |
| 30. C2×ΓL(1,𝔽25) | C22 | semidirect |
| 37. C22×SD16 | D3 | semidirect |
| 53. D3×Q8 | C23 | semidirect |
| 64. C3×SD16 | C23 | semidirect |
| 66. #216 | C23 | semidirect |
| 67. #214 | C23 | semidirect |
| 69. Dic12 | C23 | semidirect |
| 70. ΓL(1,𝔽25) | C23 | semidirect |
| 88. C2×SD16 | C2×D3 | semidirect |
| 147. SD16 | C22×D3 | semidirect |
| 153. C22×C3 | #137 | semidirect |
| 191. C2×C3 | C2×#137 | semidirect |
| 198. C22 | #915 | direct (N × H) |
| 206. C3 | C22×#137 | semidirect |
| 209. C2 | C2×#915 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×Q8 | 2 |
| C22×#237 | 2 |
| C22×C3×SD16 | 2 |
| C22×#216 | 2 |
| C22×#214 | 2 |
| C2×#915 | 2 |
| C22×Dic12 | 2 |
| C22×ΓL(1,𝔽25) | 2 |
| C22×#137 | 3 |