Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
266 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 151 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×C3×C8 | C2 | semidirect |
| 3. C2×#208 | C2 | semidirect |
| 4. #901 | C2 | direct (N × H) |
| 5. C2×ΓL(1,𝔽25) | C2 | semidirect |
| 6. C2×D3×C8 | C2 | semidirect |
| 17. C2×C3×C8 | C22 | semidirect |
| 18. #208 | C22 | semidirect |
| 20. ΓL(1,𝔽25) | C22 | semidirect |
| 21. D3×C8 | C22 | semidirect |
| 27. C22×C8 | D3 | semidirect |
| 56. C2×C8 | C2×D3 | semidirect |
| 82. C2×C3 | #131 | semidirect |
| 94. C3 | C2×#131 | semidirect |
| 97. C2 | #901 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#235 | 2 |
| C22×C3×C8 | 2 |
| C2×#208 | 2 |
| #901 | 2 |
| C2×ΓL(1,𝔽25) | 2 |
| C2×D3×C8 | 2 |
| C2×#131 | 3 |