Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 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. C22×C3×Q8 | C2 | semidirect |
| 3. C2×#216 | C2 | semidirect |
| 4. #942 | C2 | direct (N × H) |
| 5. C2×#215 | C2 | semidirect |
| 6. C2×#208 | C2 | semidirect |
| 11. C2×C3×Q8 | C22 | semidirect |
| 20. #216 | C22 | semidirect |
| 21. #215 | C22 | semidirect |
| 22. #208 | C22 | semidirect |
| 25. C22×Q8 | D3 | semidirect |
| 55. C2×Q8 | C2×D3 | semidirect |
| 95. C2×C3 | #137 | semidirect |
| 108. C3 | C2×#137 | semidirect |
| 111. C2 | #942 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Q8 | 2 |
| C2×#235 | 2 |
| C2×#216 | 2 |
| #942 | 2 |
| C2×#215 | 2 |
| C2×#208 | 2 |
| C2×#137 | 3 |