Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 43 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. #944 | C2 | semidirect |
| 4. C2×#216 | C2 | semidirect |
| 7. #815 | C2 | semidirect |
| 23. C2×Q16 | D3 | semidirect |
| 95. C3 | #497 | 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 |
| #944 | 2 |
| C2×#216 | 2 |
| C2×#215 | 2 |
| C2×#204 | 2 |
| #815 | 2 |
| #497 | 3 |