Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
122 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 59 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. Q8×Dic3 | C2 | semidirect |
| 4. #835 | C2 | semidirect |
| 6. #817 | C2 | semidirect |
| 7. C8×Dic3 | C2 | semidirect |
| 12. C3×SD16 | C4 | semidirect |
| 30. C3×Q8 | C2×C4 | semidirect |
| 40. C3×C8 | C2×C4 | semidirect |
| 45. SD16 | Dic3 | direct (N × H) |
| 64. Dic3 | SD16 | direct (N × H) |
| 67. Q8 | C2×Dic3 | semidirect |
| 78. C8 | C2×Dic3 | semidirect |
| 94. C3 | C4×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×SD16 | 2 |
| Q8×Dic3 | 2 |
| D4×Dic3 | 2 |
| #835 | 2 |
| #832 | 2 |
| #817 | 2 |
| C8×Dic3 | 2 |
| C4×SD16 | 3 |