Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
122 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4 | D4 |
| commutator | C4 | C22×C3×C4 |
| Frattini, cosocle | C2×C4 | C23×C3 |
| socle | C22×C3 | C2×D4 |
| prime radical | C2×C3×D4 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4 ◁ C3×C42 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C4×Q8 | C2 | semidirect |
| 4. C3×#106 | C2 | semidirect |
| 5. C3×#103 | C2 | semidirect |
| 7. C3×C4×C8 | C2 | semidirect |
| 8. C4×SD16 | C3 | direct (N × H) |
| 12. C3×SD16 | C4 | direct (N × H) |
| 22. C4×Q8 | C2×C3 | semidirect |
| 24. #106 | C2×C3 | semidirect |
| 25. #103 | C2×C3 | semidirect |
| 27. C4×C8 | C2×C3 | semidirect |
| 30. C3×Q8 | C2×C4 | semidirect |
| 41. C3×C8 | C2×C4 | semidirect |
| 45. SD16 | C3×C4 | direct (N × H) |
| 62. C3×C4 | SD16 | direct (N × H) |
| 67. Q8 | C2×C3×C4 | semidirect |
| 78. C8 | C2×C3×C4 | semidirect |
| 91. C4 | C3×SD16 | direct (N × H) |
| 94. C3 | C4×SD16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×SD16 | 2 |
| C3×C4×Q8 | 2 |
| C3×C4×D4 | 2 |
| C3×#106 | 2 |
| C3×#103 | 2 |
| C3×#102 | 2 |
| C3×C4×C8 | 2 |
| C4×SD16 | 3 |