Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
150 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 150 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 |
|---|---|---|
| 4. C3×#103 | C2 | semidirect |
| 5. #835 | C2 | semidirect |
| 6. #816 | C2 | semidirect |
| 7. #810 | C2 | semidirect |
| 11. D3×Q8 | C4 | semidirect |
| 29. #103 | D3 | semidirect |
| 104. C3 | #419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Q8 | 2 |
| C2×ΓL(1,𝔽25) | 2 |
| #892 | 2 |
| C3×#103 | 2 |
| #835 | 2 |
| #816 | 2 |
| #810 | 2 |
| #419 | 3 |