Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D3×D4 |
| commutator, cosocle | C3×C4 | C24 |
| Frattini | C4 | C23×D3 |
| Fitting | C3×#135 | C2 |
| socle | C2×C3 | C22×D4 |
| hypercenter | #135 | D3 |
| hypocenter | C3 | #578 |
| LCS | G ▷ C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #135 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #1010 | C2 | semidirect |
| 2. C3×#135 | C2 | semidirect |
| 3. #951 | C2 | semidirect |
| 4. D3×Q16 | C2 | semidirect |
| 5. #915 | C2 | semidirect |
| 6. #912 | C2 | semidirect |
| 7. C2×Dic12 | C2 | semidirect |
| 8. #901 | C2 | semidirect |
| 33. #135 | D3 | semidirect |
| 114. C3 | #578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #1010 | 2 |
| C3×#135 | 2 |
| #951 | 2 |
| D3×Q16 | 2 |
| #915 | 2 |
| #912 | 2 |
| C2×Dic12 | 2 |
| #901 | 2 |
| #578 | 3 |