Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 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×#121 | C2 |
| hypercenter | #121 | D3 |
| hypocenter | C3 | #538 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#121 | C2 | semidirect |
| 2. #939 | C2 | semidirect |
| 3. #937 | C2 | semidirect |
| 4. D4×Dic3 | C2 | semidirect |
| 5. C2×(C2×D3)⋊C4 | C2 | semidirect |
| 6. #924 | C2 | semidirect |
| 7. #898 | C2 | semidirect |
| 8. #886 | C2 | semidirect |
| 9. #885 | C2 | semidirect |
| 13. C2×C3×D4 | C22 | semidirect |
| 18. C22×Dic3 | C22 | semidirect |
| 19. C2×Dic6 | C22 | semidirect |
| 20. C3×C4⋊C4 | C22 | semidirect |
| 21. C3×C22⋊C4 | C22 | semidirect |
| 23. #217 | C22 | semidirect |
| 28. C4⋊Dic3 | C22 | semidirect |
| 29. C4⋊Dic3 | C22 | semidirect |
| 30. Dic3⋊C4 | C22 | semidirect |
| 31. C4×Dic3 | C22 | semidirect |
| 37. #121 | D3 | semidirect |
| 66. C2×D4 | C2×D3 | semidirect |
| 73. C4⋊C4 | C2×D3 | semidirect |
| 80. C22⋊C4 | C2×D3 | semidirect |
| 142. C3 | #538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#121 | 2 |
| #939 | 2 |
| #937 | 2 |
| D4×Dic3 | 2 |
| C2×(C2×D3)⋊C4 | 2 |
| #924 | 2 |
| #898 | 2 |
| #886 | 2 |
| #885 | 2 |
| #538 | 3 |