Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
198 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 51 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×D4 | C2 | semidirect |
| 2. C2×#213 | C2 | semidirect |
| 3. #930 | C2 | semidirect |
| 4. #832 | C2 | semidirect |
| 5. #830 | C2 | semidirect |
| 13. C2×D12 | C22 | semidirect |
| 16. C4⋊Dic3 | C22 | semidirect |
| 17. C2×C3⋊C8 | C22 | semidirect |
| 18. C22×D4 | D3 | semidirect |
| 31. C3×D4 | D4 | semidirect |
| 56. C22×C3 | D8 | semidirect |
| 74. D4 | #67 | semidirect |
| 95. C22 | #213 | semidirect |
| 100. C3 | #447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D4 | 2 |
| C2×#213 | 2 |
| #930 | 2 |
| #832 | 2 |
| #830 | 2 |
| #447 | 3 |