Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 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×#127 | C2 |
| hypercenter | #127 | D3 |
| hypocenter | C3 | #535 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#237 | C2 | semidirect |
| 2. C2×D3×D4 | C2 | semidirect |
| 3. C3×#127 | C2 | semidirect |
| 4. #940 | C2 | semidirect |
| 5. #939 | C2 | semidirect |
| 6. #937 | C2 | semidirect |
| 7. #936 | C2 | semidirect |
| 8. #875 | C2 | semidirect |
| 9. #872 | C2 | semidirect |
| 13. C2×C3×D4 | C22 | semidirect |
| 14. C2×C3×D4 | C22 | semidirect |
| 17. C2×#67 | C22 | semidirect |
| 18. C22×Dic3 | C22 | semidirect |
| 23. C2×Dic6 | C22 | semidirect |
| 24. C3×C42 | C22 | semidirect |
| 25. #217 | C22 | semidirect |
| 27. (C2×D3)⋊C4 | C22 | semidirect |
| 28. Dic3⋊C4 | C22 | semidirect |
| 29. C4×Dic3 | C22 | semidirect |
| 33. #127 | D3 | semidirect |
| 58. C4×D3 | D4 | semidirect |
| 69. C2×D4 | C2×D3 | semidirect |
| 70. C2×D4 | C2×D3 | semidirect |
| 78. C42 | C2×D3 | semidirect |
| 136. C3 | #535 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#237 | 2 |
| C2×D3×D4 | 2 |
| C3×#127 | 2 |
| #940 | 2 |
| #939 | 2 |
| #937 | 2 |
| #936 | 2 |
| #875 | 2 |
| #872 | 2 |
| #535 | 3 |