Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
310 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 310 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 | C3×#127 | C2 |
| hypercenter | #127 | D3 |
| hypocenter | C3 | #532 |
| 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. #938 | C2 | semidirect |
| 4. #936 | C2 | semidirect |
| 5. D4×Dic3 | C2 | semidirect |
| 6. C42×D3 | C2 | semidirect |
| 7. #869 | C2 | semidirect |
| 24. #127 | D3 | semidirect |
| 41. C4×D3 | D4 | semidirect |
| 62. C3×C4 | #41 | semidirect |
| 93. C4 | #237 | semidirect |
| 94. C3 | #532 | 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 |
| #938 | 2 |
| #936 | 2 |
| D4×Dic3 | 2 |
| C42×D3 | 2 |
| #869 | 2 |
| #532 | 3 |