Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
132 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 132 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. C3×C4×D4 | C2 | semidirect |
| 3. C4×D12 | C2 | semidirect |
| 4. #832 | C2 | semidirect |
| 5. #809 | C2 | semidirect |
| 6. #808 | C2 | semidirect |
| 7. #803 | C2 | semidirect |
| 16. #213 | C4 | semidirect |
| 23. C4×D4 | D3 | semidirect |
| 31. C3×D4 | C2×C4 | semidirect |
| 39. D12 | C2×C4 | semidirect |
| 42. C3⋊C8 | C2×C4 | semidirect |
| 73. D4 | C4×D3 | semidirect |
| 101. C3 | #442 | 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×#213 | 2 |
| C4×D12 | 2 |
| #832 | 2 |
| #809 | 2 |
| #808 | 2 |
| #803 | 2 |
| #442 | 3 |