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. C3×C4×D4 | C2 | semidirect |
| 2. C2×#214 | C2 | semidirect |
| 4. #875 | C2 | semidirect |
| 5. #810 | C2 | semidirect |
| 6. #809 | C2 | semidirect |
| 7. C4⋊(C3⋊C8) | C2 | semidirect |
| 25. C4×D4 | D3 | semidirect |
| 105. C3 | #463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D4 | 2 |
| C2×#214 | 2 |
| C2×#213 | 2 |
| #875 | 2 |
| #810 | 2 |
| #809 | 2 |
| C4⋊(C3⋊C8) | 2 |
| #463 | 3 |