Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
322 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 121 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×D3 | C22 |
| hypercenter | C22⋊Q8 | D3 |
| hypocenter | C3 | C2×C22⋊Q8 |
| 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 |
|---|---|---|
| 1. C2×D3×Q8 | C2 | semidirect |
| 3. C3×C22⋊Q8 | C2 | semidirect |
| 4. #946 | C2 | semidirect |
| 5. #924 | C2 | semidirect |
| 6. #897 | C2 | semidirect |
| 7. #896 | C2 | semidirect |
| 8. D3×C4⋊C4 | C2 | semidirect |
| 9. D3×C4⋊C4 | C2 | semidirect |
| 11. #878 | C2 | semidirect |
| 14. C2×C3×Q8 | C22 | semidirect |
| 25. C2×Dic6 | C22 | semidirect |
| 26. C2×Dic6 | C22 | semidirect |
| 27. C3×C4⋊C4 | C22 | semidirect |
| 28. C3×C4⋊C4 | C22 | semidirect |
| 33. C4⋊Dic3 | C22 | semidirect |
| 34. C4⋊Dic3 | C22 | semidirect |
| 35. Dic3⋊C4 | C22 | semidirect |
| 36. Dic3⋊C4 | C22 | semidirect |
| 37. Dic3⋊C4 | C22 | semidirect |
| 45. C22⋊Q8 | D3 | direct (N × H) |
| 52. C22×D3 | Q8 | semidirect |
| 78. C2×Q8 | C2×D3 | semidirect |
| 93. C4⋊C4 | C2×D3 | semidirect |
| 94. C4⋊C4 | C2×D3 | semidirect |
| 101. C22×C3 | C2×Q8 | semidirect |
| 108. C2×D3 | C2×Q8 | semidirect |
| 148. D3 | C22⋊Q8 | direct (N × H) |
| 158. C22 | D3×Q8 | semidirect |
| 168. C3 | C2×C22⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Q8 | 2 |
| C22×C4×D3 | 2 |
| C3×C22⋊Q8 | 2 |
| #946 | 2 |
| #924 | 2 |
| #897 | 2 |
| #896 | 2 |
| D3×C4⋊C4 | 2 |
| D3×C22⋊C4 | 2 |
| #878 | 2 |
| C2×C22⋊Q8 | 3 |