Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
330 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 119 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 | C23×C3×C4 | C2 |
| hypercenter | C23×C4 | D3 |
| hypocenter | C3 | #525 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C4 ◁ C23×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C3×C4 | C2 | semidirect |
| 2. C2×#235 | C2 | semidirect |
| 3. #953 | C2 | semidirect |
| 4. #930 | C2 | semidirect |
| 5. #929 | C2 | semidirect |
| 6. C4×#67 | C2 | semidirect |
| 7. #926 | C2 | semidirect |
| 8. #924 | C2 | semidirect |
| 19. C2×D12 | C22 | semidirect |
| 20. C2×C4×D3 | C22 | semidirect |
| 21. C2×Dic6 | C22 | semidirect |
| 24. (C2×D3)⋊C4 | C22 | semidirect |
| 25. C4⋊Dic3 | C22 | semidirect |
| 26. Dic3⋊C4 | C22 | semidirect |
| 27. C4×Dic3 | C22 | semidirect |
| 29. C23×C4 | D3 | semidirect |
| 44. C2×C3×C4 | D4 | semidirect |
| 78. C22×C3 | #41 | semidirect |
| 102. C2×C4 | #67 | semidirect |
| 117. C22 | #235 | semidirect |
| 125. C3 | #525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C4 | 2 |
| C2×#235 | 2 |
| #953 | 2 |
| #930 | 2 |
| #929 | 2 |
| C4×#67 | 2 |
| #926 | 2 |
| #924 | 2 |
| #525 | 3 |