Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
292 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 113 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 | C2×C3×#41 | C2 |
| hypercenter | C2×#41 | D3 |
| hypocenter | C3 | #547 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×#41 | C2 | semidirect |
| 2. C2×#237 | C2 | semidirect |
| 3. #946 | C2 | semidirect |
| 4. #944 | C2 | semidirect |
| 5. #939 | C2 | semidirect |
| 6. #935 | C2 | semidirect |
| 7. D4×Dic3 | C2 | semidirect |
| 8. #929 | C2 | semidirect |
| 9. C4×#67 | C2 | semidirect |
| 10. #924 | C2 | semidirect |
| 11. C2×Dic3⋊C4 | C2 | semidirect |
| 39. C2×#41 | D3 | semidirect |
| 54. C3×D4 | D4 | semidirect |
| 113. Dic3 | #41 | semidirect |
| 122. D4 | #67 | semidirect |
| 160. C3 | #547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#41 | 2 |
| C2×#237 | 2 |
| #946 | 2 |
| #944 | 2 |
| #939 | 2 |
| #935 | 2 |
| D4×Dic3 | 2 |
| #929 | 2 |
| C4×#67 | 2 |
| #924 | 2 |
| C2×Dic3⋊C4 | 2 |
| #547 | 3 |