Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 122 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 |
|---|---|---|
| 3. C4×Dic6 | C2 | semidirect |
| 5. #810 | C2 | semidirect |
| 6. #808 | C2 | semidirect |
| 7. C4×C3⋊C8 | C2 | semidirect |
| 15. #214 | C4 | direct (N × H) |
| 39. Dic6 | C2×C4 | semidirect |
| 41. C3⋊C8 | C2×C4 | semidirect |
| 60. C3×C4 | SD16 | semidirect |
| 91. C4 | #214 | direct (N × H) |
| 94. C3 | C4×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D4 | 2 |
| C2×#214 | 2 |
| C4×Dic6 | 2 |
| #832 | 2 |
| #810 | 2 |
| #808 | 2 |
| C4×C3⋊C8 | 2 |
| C4×SD16 | 3 |