Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
258 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×D3×Q8 | C2 | semidirect |
| 3. C2×C3×Q16 | C2 | semidirect |
| 4. C2×#216 | C2 | semidirect |
| 5. C2×#215 | C2 | semidirect |
| 6. #918 | C2 | direct (N × H) |
| 7. C2×#204 | C2 | semidirect |
| 8. C2×ΓL(1,𝔽25) | C2 | semidirect |
| 15. D3×Q8 | C22 | semidirect |
| 23. C3×Q16 | C22 | semidirect |
| 25. #216 | C22 | semidirect |
| 26. #215 | C22 | semidirect |
| 28. #204 | C22 | semidirect |
| 29. ΓL(1,𝔽25) | C22 | semidirect |
| 34. C2×Q16 | D3 | semidirect |
| 75. Q16 | C2×D3 | semidirect |
| 115. C2×C3 | #137 | semidirect |
| 130. C3 | C2×#137 | semidirect |
| 133. C2 | #918 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#239 | 2 |
| C2×D3×Q8 | 2 |
| C2×C3×Q16 | 2 |
| C2×#216 | 2 |
| C2×#215 | 2 |
| #918 | 2 |
| C2×#204 | 2 |
| C2×ΓL(1,𝔽25) | 2 |
| C2×#137 | 3 |