Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
317 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 317 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×A4 |
| commutator, cosocle | C23 | C23×C3 |
| Frattini | C2 | C23×A4 |
| Fitting | C23×D4 | C3 |
| socle | C24 | C22×C3 |
| hypercenter | C2×D4 | A4 |
| hypocenter | C22 | C2×C3×D4 |
| LCS | G ▷ C23 ▷ C22 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×A4 | C2 | semidirect |
| 2. D4×A4 | C2 | direct (N × H) |
| 3. C2×C4×A4 | C2 | semidirect |
| 4. C23×D4 | C3 | semidirect |
| 7. C22×A4 | C22 | semidirect |
| 9. C4×A4 | C22 | semidirect |
| 10. C25 | C2×C3 | semidirect |
| 15. C22×D4 | C2×C3 | semidirect |
| 16. C23×C4 | C2×C3 | semidirect |
| 19. C2×A4 | D4 | direct (N × H) |
| 29. C24 | C22×C3 | semidirect |
| 39. C2×D4 | A4 | direct (N × H) |
| 43. C22×C4 | C22×C3 | semidirect |
| 47. A4 | C2×D4 | direct (N × H) |
| 65. C23 | C3×D4 | semidirect |
| 66. C23 | C2×A4 | semidirect |
| 71. D4 | C2×A4 | direct (N × H) |
| 77. C2×C4 | C2×A4 | semidirect |
| 97. C22 | C2×C3×D4 | semidirect |
| 99. C22 | C22×A4 | semidirect |
| 101. C4 | C22×A4 | semidirect |
| 108. C2 | D4×A4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×A4 | 2 |
| D4×A4 | 2 |
| C2×C4×A4 | 2 |
| C23×D4 | 3 |
| C2×C3×D4 | 4 |