Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
268 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×#67 |
| commutator, cosocle | C3×C4 | C24 |
| Frattini | C4 | C23×D3 |
| Fitting | C3×H(5,𝔽2) | C2 |
| socle | C2×C3 | C22×D4 |
| hypercenter | H(5,𝔽2) | D3 |
| hypocenter | C3 | #576 |
| LCS | G ▷ C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ H(5,𝔽2) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×H(5,𝔽2) | C2 | semidirect |
| 2. #1009 | C2 | semidirect |
| 3. #950 | C2 | semidirect |
| 4. #949 | C2 | semidirect |
| 5. #948 | C2 | semidirect |
| 6. #932 | C2 | semidirect |
| 7. C2×#213 | C2 | semidirect |
| 11. C3×#41 | C22 | semidirect |
| 13. C2×C3×D4 | C22 | semidirect |
| 16. #235 | C22 | semidirect |
| 17. C2×D12 | C22 | semidirect |
| 18. #216 | C22 | semidirect |
| 19. #215 | C22 | semidirect |
| 20. #214 | C22 | semidirect |
| 21. #213 | C22 | semidirect |
| 22. #213 | C22 | semidirect |
| 23. #208 | C22 | semidirect |
| 24. C2×C3⋊C8 | C22 | semidirect |
| 26. H(5,𝔽2) | D3 | semidirect |
| 53. #41 | C2×D3 | semidirect |
| 57. C2×D4 | C2×D3 | semidirect |
| 104. C3 | #576 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×H(5,𝔽2) | 2 |
| #1009 | 2 |
| #950 | 2 |
| #949 | 2 |
| #948 | 2 |
| #932 | 2 |
| C2×#213 | 2 |
| #576 | 3 |