Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 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 |
| hypercenter | C22⋊Q8 | D3 |
| hypocenter | C3 | #525 |
| 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×#239 | C2 | semidirect |
| 2. C22×C4×D3 | C2 | semidirect |
| 3. C3×C22⋊Q8 | C2 | semidirect |
| 4. #946 | C2 | semidirect |
| 5. #930 | C2 | semidirect |
| 6. #895 | C2 | semidirect |
| 7. #894 | C2 | semidirect |
| 8. #893 | C2 | semidirect |
| 9. #892 | C2 | semidirect |
| 10. #882 | C2 | semidirect |
| 11. #67⋊C4 | C2 | semidirect |
| 14. C2×C3×Q8 | C22 | semidirect |
| 21. C2×D12 | C22 | semidirect |
| 27. C2×C4×D3 | C22 | semidirect |
| 28. C3×C4⋊C4 | C22 | semidirect |
| 29. C3×C4⋊C4 | C22 | semidirect |
| 33. (C2×D3)⋊C4 | C22 | semidirect |
| 34. (C2×D3)⋊C4 | C22 | semidirect |
| 35. C4⋊Dic3 | C22 | semidirect |
| 36. Dic3⋊C4 | C22 | semidirect |
| 37. C4×Dic3 | C22 | semidirect |
| 42. C22⋊Q8 | D3 | semidirect |
| 74. C4×D3 | D4 | semidirect |
| 77. C2×Q8 | C2×D3 | semidirect |
| 92. C4⋊C4 | C2×D3 | semidirect |
| 93. C4⋊C4 | C2×D3 | semidirect |
| 102. C22×C3 | #41 | semidirect |
| 113. C2×D3 | #41 | semidirect |
| 166. C22 | #239 | semidirect |
| 175. C3 | #525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#239 | 2 |
| C22×C4×D3 | 2 |
| C3×C22⋊Q8 | 2 |
| #946 | 2 |
| #930 | 2 |
| #895 | 2 |
| #894 | 2 |
| #893 | 2 |
| #892 | 2 |
| #882 | 2 |
| #67⋊C4 | 2 |
| #525 | 3 |