Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
312 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 107 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 | #550 |
| 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. C3×#127 | C2 | semidirect |
| 3. #940 | C2 | semidirect |
| 4. #939 | C2 | semidirect |
| 5. #938 | C2 | semidirect |
| 6. D4×Dic3 | C2 | semidirect |
| 7. C4×D12 | C2 | semidirect |
| 8. C4×Dic6 | C2 | semidirect |
| 29. #127 | D3 | semidirect |
| 51. Dic6 | D4 | semidirect |
| 78. C3×C4 | #41 | semidirect |
| 116. C4 | #237 | semidirect |
| 117. C3 | #550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#237 | 2 |
| C3×#127 | 2 |
| #940 | 2 |
| #939 | 2 |
| #938 | 2 |
| D4×Dic3 | 2 |
| C4×D12 | 2 |
| C4×Dic6 | 2 |
| #550 | 3 |