Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
294 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 151 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 | C2×C3 | C23×C4 |
| Fitting | C3×C4×D4 | C2 |
| socle, cosocle | C22×C3 | C24 |
| prime radical | C2×#237 | C2 |
| hypercenter | C4×D4 | D3 |
| hypocenter | C3 | #520 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C4×D4 | C2 | semidirect |
| 3. D4×Dic3 | C2 | semidirect |
| 4. C4×#67 | C2 | semidirect |
| 5. C2×Dic3⋊C4 | C2 | semidirect |
| 6. D3×C4⋊C4 | C2 | semidirect |
| 7. #887 | C2 | semidirect |
| 8. #67⋊C4 | C2 | semidirect |
| 9. #877 | C2 | semidirect |
| 10. #872 | C2 | semidirect |
| 11. C4×Dic6 | C2 | semidirect |
| 18. #237 | C4 | semidirect |
| 43. C4×D4 | D3 | semidirect |
| 50. C3×D4 | C2×C4 | semidirect |
| 56. #67 | C2×C4 | semidirect |
| 58. C2×Dic3 | C2×C4 | semidirect |
| 65. C4×D3 | C2×C4 | semidirect |
| 66. Dic6 | C2×C4 | semidirect |
| 111. D4 | C4×D3 | semidirect |
| 147. C3 | #520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#237 | 2 |
| C3×C4×D4 | 2 |
| D4×Dic3 | 2 |
| C4×#67 | 2 |
| C2×Dic3⋊C4 | 2 |
| D3×C4⋊C4 | 2 |
| #887 | 2 |
| #67⋊C4 | 2 |
| #877 | 2 |
| #872 | 2 |
| C4×Dic6 | 2 |
| #520 | 3 |