Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
222 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D3 |
| commutator, socle, cosocle | C22×C3 | C24 |
| Frattini | C22 | C23×D3 |
| Fitting | C3×C4×Q8 | C2 |
| prime radical | C22×D3 | C23 |
| hypercenter | C4×Q8 | D3 |
| hypocenter | C3 | #533 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C4 ◁ C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C4×Q8 | C2 | semidirect |
| 3. #944 | C2 | semidirect |
| 6. #889 | C2 | semidirect |
| 7. #888 | C2 | semidirect |
| 10. C4×Dic6 | C2 | semidirect |
| 11. C4×Dic6 | C2 | semidirect |
| 44. C4×Q8 | D3 | semidirect |
| 61. C4×D3 | Q8 | semidirect |
| 136. C3 | #533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×Q8 | 2 |
| #946 | 2 |
| #944 | 2 |
| #897 | 2 |
| #896 | 2 |
| #889 | 2 |
| #888 | 2 |
| #872 | 2 |
| C42×D3 | 2 |
| C4×Dic6 | 2 |
| #533 | 3 |