Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
310 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 157 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. C3×C4×D4 | C2 | semidirect |
| 3. D4×Dic3 | C2 | semidirect |
| 4. C4×#67 | C2 | semidirect |
| 5. C2×C4×Dic3 | C2 | semidirect |
| 6. #892 | C2 | semidirect |
| 7. #887 | C2 | semidirect |
| 8. #67⋊C4 | C2 | semidirect |
| 9. #877 | C2 | semidirect |
| 10. C42×D3 | C2 | semidirect |
| 11. C4×Dic6 | C2 | semidirect |
| 18. #237 | C4 | direct (N × H) |
| 43. C4×D4 | D3 | semidirect |
| 50. C3×D4 | C2×C4 | semidirect |
| 56. #67 | C2×C4 | semidirect |
| 58. C2×Dic3 | C2×C4 | semidirect |
| 66. C4×D3 | C2×C4 | semidirect |
| 67. Dic6 | C2×C4 | semidirect |
| 102. C3×C4 | #41 | semidirect |
| 107. Dic3 | #41 | semidirect |
| 112. D4 | C4×D3 | semidirect |
| 148. C4 | #237 | direct (N × H) |
| 149. C3 | C4×#41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#237 | 2 |
| C3×C4×D4 | 2 |
| D4×Dic3 | 2 |
| C4×#67 | 2 |
| C2×C4×Dic3 | 2 |
| #892 | 2 |
| #887 | 2 |
| #67⋊C4 | 2 |
| #877 | 2 |
| C42×D3 | 2 |
| C4×Dic6 | 2 |
| C4×#41 | 3 |