Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
330 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D3 |
| commutator, socle, cosocle | C22×C3 | C24 |
| Frattini | C22 | C23×D3 |
| Fitting | C3×#117 | C2 |
| hypercenter | #117 | D3 |
| hypocenter | C3 | #525 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C4 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#235 | C2 | semidirect |
| 2. C22×C4×D3 | C2 | semidirect |
| 3. C3×#117 | C2 | semidirect |
| 4. #897 | C2 | semidirect |
| 5. #895 | C2 | semidirect |
| 6. #886 | C2 | semidirect |
| 7. #882 | C2 | semidirect |
| 8. C4×D12 | C2 | semidirect |
| 16. C2×D12 | C22 | semidirect |
| 20. C2×C4×D3 | C22 | semidirect |
| 21. C2×Dic6 | C22 | semidirect |
| 22. C3×C4⋊C4 | C22 | semidirect |
| 24. C3×C42 | C22 | semidirect |
| 26. (C2×D3)⋊C4 | C22 | semidirect |
| 27. C4⋊Dic3 | C22 | semidirect |
| 35. #117 | D3 | semidirect |
| 41. C2×C3×C4 | D4 | semidirect |
| 68. C4⋊C4 | C2×D3 | semidirect |
| 72. C42 | C2×D3 | semidirect |
| 81. C2×D3 | #41 | semidirect |
| 102. C2×C4 | D12 | semidirect |
| 125. C3 | #525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#235 | 2 |
| C22×C4×D3 | 2 |
| C3×#117 | 2 |
| #897 | 2 |
| #895 | 2 |
| #886 | 2 |
| #882 | 2 |
| C4×D12 | 2 |
| #525 | 3 |