Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×#216 | C2 | semidirect |
| 3. C2×Dic12 | C2 | semidirect |
| 5. C3×#103 | C2 | semidirect |
| 7. #810 | C2 | semidirect |
| 29. #103 | D3 | semidirect |
| 68. C2×D3 | Q16 | semidirect |
| 110. C3 | #451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Q8 | 2 |
| C2×#216 | 2 |
| C2×Dic12 | 2 |
| #897 | 2 |
| C3×#103 | 2 |
| (C2×D3)⋊C8 | 2 |
| #810 | 2 |
| #451 | 3 |