Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
266 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 266 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 | C22 | D3×D4 |
| commutator, cosocle | C3×C4 | C24 |
| Frattini | C4 | C23×D3 |
| Fitting | C2×C3×SD16 | C2 |
| socle | C22×C3 | C2×D4 |
| hypercenter | C2×SD16 | D3 |
| hypocenter | C3 | C2×#135 |
| LCS | G ▷ C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×SD16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#239 | C2 | semidirect |
| 2. C2×#237 | C2 | semidirect |
| 3. C2×C3×SD16 | C2 | semidirect |
| 4. C2×#216 | C2 | semidirect |
| 5. C2×#213 | C2 | semidirect |
| 6. #916 | C2 | direct (N × H) |
| 7. C2×#204 | C2 | semidirect |
| 8. C2×D3×C8 | C2 | semidirect |
| 15. #239 | C22 | semidirect |
| 17. #237 | C22 | semidirect |
| 23. C3×SD16 | C22 | semidirect |
| 25. #216 | C22 | semidirect |
| 26. #213 | C22 | semidirect |
| 28. #204 | C22 | semidirect |
| 29. D3×C8 | C22 | semidirect |
| 35. C2×SD16 | D3 | semidirect |
| 76. SD16 | C2×D3 | semidirect |
| 117. C2×C3 | #135 | semidirect |
| 133. C3 | C2×#135 | semidirect |
| 137. C2 | #916 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#239 | 2 |
| C2×#237 | 2 |
| C2×C3×SD16 | 2 |
| C2×#216 | 2 |
| C2×#213 | 2 |
| #916 | 2 |
| C2×#204 | 2 |
| C2×D3×C8 | 2 |
| C2×#135 | 3 |