Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
112 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 41 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. C2×C3×Q16 | C2 | semidirect |
| 3. Q8×Dic3 | C2 | semidirect |
| 5. #835 | C2 | semidirect |
| 7. Dic3⋊C8 | C2 | semidirect |
| 22. C2×Q16 | D3 | semidirect |
| 98. C3 | #464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q16 | 2 |
| #947 | 2 |
| Q8×Dic3 | 2 |
| C2×#215 | 2 |
| #835 | 2 |
| #821 | 2 |
| Dic3⋊C8 | 2 |
| #464 | 3 |