Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
342 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 127 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. C23×C3×C4 | C2 | semidirect |
| 3. C2×#217 | C2 | semidirect |
| 4. #929 | C2 | direct (N × H) |
| 5. C2×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C2×Dic3⋊C4 | C2 | semidirect |
| 12. C22×C3×C4 | C22 | semidirect |
| 17. #217 | C22 | semidirect |
| 18. (C2×D3)⋊C4 | C22 | semidirect |
| 19. Dic3⋊C4 | C22 | semidirect |
| 21. C23×C4 | D3 | semidirect |
| 49. C22×C4 | C2×D3 | semidirect |
| 81. C2×C3 | #123 | semidirect |
| 97. C3 | C2×#123 | semidirect |
| 100. C2 | #929 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C4 | 2 |
| C22×#67 | 2 |
| C2×#217 | 2 |
| #929 | 2 |
| C2×(C2×D3)⋊C4 | 2 |
| C2×Dic3⋊C4 | 2 |
| C2×#123 | 3 |