Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
426 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D3 |
| commutator, cosocle | C22×C3 | C24 |
| Frattini | C22 | C23×D3 |
| Fitting | C22×C3×D4 | C2 |
| socle | C23×C3 | C23 |
| hypercenter | C22×D4 | D3 |
| hypocenter | C3 | C2×#121 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3×D4 | C2 | semidirect |
| 2. C22×#67 | C2 | semidirect |
| 3. C22×#67 | C2 | semidirect |
| 4. C23×Dic3 | C2 | semidirect |
| 5. C2×#217 | C2 | semidirect |
| 6. #939 | C2 | direct (N × H) |
| 7. C2×(C2×D3)⋊C4 | C2 | semidirect |
| 8. C2×Dic3⋊C4 | C2 | semidirect |
| 14. C2×C3×D4 | C22 | semidirect |
| 18. C2×#67 | C22 | semidirect |
| 19. C2×#67 | C22 | semidirect |
| 24. C22×Dic3 | C22 | semidirect |
| 25. #217 | C22 | semidirect |
| 26. (C2×D3)⋊C4 | C22 | semidirect |
| 27. Dic3⋊C4 | C22 | semidirect |
| 30. C22×D4 | D3 | semidirect |
| 41. C23×C3 | D4 | semidirect |
| 57. C2×Dic3 | D4 | semidirect |
| 69. C2×D4 | C2×D3 | semidirect |
| 88. C22×C3 | C2×D4 | semidirect |
| 98. Dic3 | C2×D4 | semidirect |
| 108. C23 | #67 | semidirect |
| 126. C2×C3 | #121 | semidirect |
| 145. C22 | C2×#67 | semidirect |
| 151. C3 | C2×#121 | semidirect |
| 155. C2 | #939 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D4 | 2 |
| C22×#67 | 2 |
| C23×Dic3 | 2 |
| C2×#217 | 2 |
| #939 | 2 |
| C2×(C2×D3)⋊C4 | 2 |
| C2×Dic3⋊C4 | 2 |
| C2×#121 | 3 |