Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
162 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 162 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. D3×C4⋊C4 | C2 | semidirect |
| 4. C3×#103 | C2 | semidirect |
| 5. #835 | C2 | semidirect |
| 6. #821 | C2 | semidirect |
| 7. #809 | C2 | semidirect |
| 11. #239 | C4 | semidirect |
| 27. #103 | D3 | semidirect |
| 33. C3×Q8 | C2×C4 | semidirect |
| 41. D12 | C2×C4 | semidirect |
| 78. Q8 | C4×D3 | semidirect |
| 111. C3 | #417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#239 | 2 |
| C2×ΓL(1,𝔽25) | 2 |
| D3×C4⋊C4 | 2 |
| C3×#103 | 2 |
| #835 | 2 |
| #821 | 2 |
| #809 | 2 |
| #417 | 3 |