Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
258 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×D3 |
| commutator, socle | C2×C3 | C23×C4 |
| Fitting | C2×C3×M16 | C2 |
| prime radical | C2×#235 | C2 |
| cosocle | C3×C4 | C24 |
| hypercenter | C2×M16 | D3 |
| hypocenter | C3 | #568 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C4 ◁ C2×M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×M16 | C2 | semidirect |
| 3. C2×#208 | C2 | semidirect |
| 4. #907 | C2 | semidirect |
| 5. D3×M16 | C2 | semidirect |
| 6. #901 | C2 | semidirect |
| 18. C3×M16 | C22 | semidirect |
| 19. C2×C3×C8 | C22 | semidirect |
| 21. #208 | C22 | semidirect |
| 22. C2×C3⋊C8 | C22 | semidirect |
| 23. ΓL(1,𝔽25) | C22 | semidirect |
| 24. D3×C8 | C22 | semidirect |
| 30. C2×M16 | D3 | semidirect |
| 63. M16 | C2×D3 | semidirect |
| 66. C2×C8 | C2×D3 | semidirect |
| 113. C3 | #568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#235 | 2 |
| C2×C3×M16 | 2 |
| C2×#208 | 2 |
| #907 | 2 |
| D3×M16 | 2 |
| #901 | 2 |
| #568 | 3 |