Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
280 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 123 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×C4×D4 | C2 |
| prime radical | C2×C3×D4 | C22 |
| hypercenter | C4×D4 | D3 |
| hypocenter | C3 | D4×Q8 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Dic6 | C2 | semidirect |
| 4. #924 | C2 | semidirect |
| 5. #888 | C2 | semidirect |
| 6. #878 | C2 | semidirect |
| 7. #869 | C2 | semidirect |
| 8. C4×Dic6 | C2 | semidirect |
| 36. C3×D4 | Q8 | semidirect |
| 48. Dic6 | D4 | direct (N × H) |
| 68. C22×C3 | C2×Q8 | semidirect |
| 73. C3×C4 | C2×Q8 | semidirect |
| 81. D4 | Dic6 | direct (N × H) |
| 97. C22 | C2×Dic6 | semidirect |
| 104. C4 | C2×Dic6 | semidirect |
| 106. C3 | D4×Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic6 | 2 |
| C3×C4×D4 | 2 |
| D4×Dic3 | 2 |
| #924 | 2 |
| #888 | 2 |
| #878 | 2 |
| #869 | 2 |
| C4×Dic6 | 2 |
| D4×Q8 | 3 |