Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
334 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 111 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 | C22×C3×D4 | C2 |
| hypercenter | C22×D4 | D3 |
| hypocenter | C3 | #535 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3×D4 | C2 | semidirect |
| 2. C2×#235 | C2 | semidirect |
| 3. #953 | C2 | semidirect |
| 4. #940 | C2 | semidirect |
| 5. #938 | C2 | semidirect |
| 6. #936 | C2 | semidirect |
| 7. #926 | C2 | semidirect |
| 15. C2×#67 | C22 | semidirect |
| 17. C2×D12 | C22 | semidirect |
| 18. C2×C4×D3 | C22 | semidirect |
| 19. C2×Dic6 | C22 | semidirect |
| 21. #217 | C22 | semidirect |
| 22. C4⋊Dic3 | C22 | semidirect |
| 23. C4×Dic3 | C22 | semidirect |
| 25. C22×D4 | D3 | semidirect |
| 38. C2×C3×C4 | D4 | semidirect |
| 89. C2×C4 | #67 | semidirect |
| 109. C3 | #535 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D4 | 2 |
| C2×#235 | 2 |
| #953 | 2 |
| #940 | 2 |
| #938 | 2 |
| #936 | 2 |
| #926 | 2 |
| #535 | 3 |