Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
426 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 194 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3 | C23 |
| commutator, Frattini, cosocle | C22 | C24×C3 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C3 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3×D4 | C2 | semidirect |
| 2. C22×C3×D4 | C2 | semidirect |
| 3. C23×C3×C4 | C2 | semidirect |
| 4. C3×#121 | C2 | direct (N × H) |
| 5. C2×C3×C4⋊C4 | C2 | semidirect |
| 6. C2×C3×C22⋊C4 | C2 | semidirect |
| 7. C2×#121 | C3 | direct (N × H) |
| 12. C2×C3×D4 | C22 | semidirect |
| 13. C2×C3×D4 | C22 | semidirect |
| 18. C22×C3×C4 | C22 | semidirect |
| 19. C3×C4⋊C4 | C22 | semidirect |
| 20. C3×C22⋊C4 | C22 | semidirect |
| 21. C22×D4 | C2×C3 | semidirect |
| 22. C22×D4 | C2×C3 | semidirect |
| 23. C23×C4 | C2×C3 | semidirect |
| 24. #121 | C2×C3 | direct (N × H) |
| 25. C2×C4⋊C4 | C2×C3 | semidirect |
| 26. C2×C22⋊C4 | C2×C3 | semidirect |
| 32. C23×C3 | D4 | semidirect |
| 41. C2×C3×C4 | D4 | semidirect |
| 49. C2×D4 | C22×C3 | semidirect |
| 50. C2×D4 | C22×C3 | semidirect |
| 55. C22×C4 | C22×C3 | semidirect |
| 56. C4⋊C4 | C22×C3 | semidirect |
| 57. C22⋊C4 | C22×C3 | semidirect |
| 67. C22×C3 | C2×D4 | semidirect |
| 72. C3×C4 | C2×D4 | semidirect |
| 78. C23 | C3×D4 | semidirect |
| 87. C2×C4 | C3×D4 | semidirect |
| 93. C2×C3 | #121 | direct (N × H) |
| 106. C22 | C2×C3×D4 | semidirect |
| 111. C4 | C2×C3×D4 | semidirect |
| 112. C3 | C2×#121 | direct (N × H) |
| 115. C2 | C3×#121 | 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 |
| C23×C3×C4 | 2 |
| C3×#121 | 2 |
| C2×C3×C4⋊C4 | 2 |
| C2×C3×C22⋊C4 | 2 |
| C2×#121 | 3 |