Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 43 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 |
|---|---|---|
| 1. C2×C3×SD16 | C2 | semidirect |
| 2. #947 | C2 | semidirect |
| 3. C2×#215 | C2 | semidirect |
| 4. #940 | C2 | semidirect |
| 5. C2×#213 | C2 | semidirect |
| 6. C2×D24 | C2 | semidirect |
| 7. #815 | C2 | semidirect |
| 23. C2×SD16 | D3 | semidirect |
| 44. C3×C8 | D4 | semidirect |
| 45. C3⋊C8 | D4 | semidirect |
| 86. C8 | #67 | semidirect |
| 103. C3 | #496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×SD16 | 2 |
| #947 | 2 |
| C2×#215 | 2 |
| #940 | 2 |
| C2×#213 | 2 |
| C2×D24 | 2 |
| #815 | 2 |
| #496 | 3 |