Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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. Q8×Dic3 | C2 | semidirect |
| 4. C3×#103 | C2 | semidirect |
| 6. #815 | C2 | semidirect |
| 7. #807 | C2 | semidirect |
| 14. #215 | C4 | semidirect |
| 25. #103 | D3 | semidirect |
| 30. C3×Q8 | C2×C4 | semidirect |
| 41. C3⋊C8 | C2×C4 | semidirect |
| 67. Q8 | C4×D3 | semidirect |
| 94. C3 | #440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic3 | 2 |
| C2×#215 | 2 |
| #893 | 2 |
| C3×#103 | 2 |
| #821 | 2 |
| #815 | 2 |
| #807 | 2 |
| #440 | 3 |