Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
158 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 55 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×ΓL(1,𝔽25) | C2 | semidirect |
| 3. C2×D3×C8 | C2 | semidirect |
| 4. C3×C22⋊C8 | C2 | semidirect |
| 5. #830 | C2 | semidirect |
| 6. (C2×D3)⋊C8 | C2 | semidirect |
| 7. (C2×D3)⋊C8 | C2 | semidirect |
| 30. C22⋊C8 | D3 | semidirect |
| 124. C3 | #408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#235 | 2 |
| C2×ΓL(1,𝔽25) | 2 |
| C2×D3×C8 | 2 |
| C3×C22⋊C8 | 2 |
| #830 | 2 |
| (C2×D3)⋊C8 | 2 |
| #408 | 3 |