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, Frattini | C22 | C23×D3 |
| commutator, socle, cosocle | C22×C3 | C24 |
| Fitting | C3×C22⋊Q8 | C2 |
| prime radical | C23×C3 | C23 |
| hypercenter | C22⋊Q8 | D3 |
| hypocenter | C3 | #533 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×Dic3 | C2 | semidirect |
| 3. #944 | C2 | semidirect |
| 6. #889 | C2 | semidirect |
| 7. #888 | C2 | semidirect |
| 8. #887 | C2 | semidirect |
| 9. #887 | C2 | semidirect |
| 55. C2×Dic3 | 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×C22⋊Q8 | 2 |
| Q8×Dic3 | 2 |
| #944 | 2 |
| #924 | 2 |
| C2×C4×Dic3 | 2 |
| #889 | 2 |
| #888 | 2 |
| #887 | 2 |
| #878 | 2 |
| #877 | 2 |
| #533 | 3 |