Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
330 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 111 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×#124 | C2 |
| prime radical | C2×D3×D4 | C2 |
| hypercenter | #124 | D3 |
| hypocenter | C3 | C2×#124 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D3×Q8 | C2 | semidirect |
| 3. C3×#124 | C2 | semidirect |
| 4. #947 | C2 | semidirect |
| 5. #936 | C2 | semidirect |
| 6. #885 | C2 | semidirect |
| 7. D3×C22⋊C4 | C2 | semidirect |
| 8. #875 | C2 | semidirect |
| 9. C42×D3 | C2 | semidirect |
| 12. C2×C3×Q8 | C22 | semidirect |
| 21. C2×Dic6 | C22 | semidirect |
| 22. C2×Dic6 | C22 | semidirect |
| 23. C3×C22⋊C4 | C22 | semidirect |
| 24. C3×C42 | C22 | semidirect |
| 25. #217 | C22 | semidirect |
| 26. (C2×D3)⋊C4 | C22 | semidirect |
| 27. (C2×D3)⋊C4 | C22 | semidirect |
| 28. C4×Dic3 | C22 | semidirect |
| 29. C4×Dic3 | C22 | semidirect |
| 36. #124 | D3 | direct (N × H) |
| 63. C2×Q8 | C2×D3 | semidirect |
| 74. C22⋊C4 | C2×D3 | semidirect |
| 77. C42 | C2×D3 | semidirect |
| 116. D3 | #124 | direct (N × H) |
| 131. C3 | C2×#124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Q8 | 2 |
| C2×D3×D4 | 2 |
| C3×#124 | 2 |
| #947 | 2 |
| #936 | 2 |
| #885 | 2 |
| D3×C22⋊C4 | 2 |
| #875 | 2 |
| C42×D3 | 2 |
| C2×#124 | 3 |