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 |
|---|---|---|
| 2. C22×D3×Q8 | C2 | semidirect |
| 3. C22×C3×Q16 | C2 | semidirect |
| 4. C22×#216 | C2 | semidirect |
| 5. C22×#215 | C2 | semidirect |
| 6. C2×#918 | C2 | direct (N × H) |
| 7. C22×#204 | C2 | semidirect |
| 8. C22×ΓL(1,𝔽25) | C2 | semidirect |
| 15. C2×D3×Q8 | C22 | semidirect |
| 23. C2×C3×Q16 | C22 | semidirect |
| 25. C2×#216 | C22 | semidirect |
| 26. C2×#215 | C22 | semidirect |
| 28. #918 | C22 | direct (N × H) |
| 29. C2×#204 | C22 | semidirect |
| 30. C2×ΓL(1,𝔽25) | C22 | semidirect |
| 35. C22×Q16 | D3 | semidirect |
| 53. D3×Q8 | C23 | semidirect |
| 64. C3×Q16 | C23 | semidirect |
| 66. #216 | C23 | semidirect |
| 67. #215 | C23 | semidirect |
| 69. #204 | C23 | semidirect |
| 70. ΓL(1,𝔽25) | C23 | semidirect |
| 86. C2×Q16 | C2×D3 | semidirect |
| 145. Q16 | C22×D3 | semidirect |
| 151. C22×C3 | #137 | semidirect |
| 190. C2×C3 | C2×#137 | semidirect |
| 198. C22 | #918 | direct (N × H) |
| 206. C3 | C22×#137 | semidirect |
| 209. C2 | C2×#918 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#239 | 2 |
| C22×D3×Q8 | 2 |
| C22×C3×Q16 | 2 |
| C22×#216 | 2 |
| C22×#215 | 2 |
| C2×#918 | 2 |
| C22×#204 | 2 |
| C22×ΓL(1,𝔽25) | 2 |
| C22×#137 | 3 |