Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
162 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | C2×D4 |
| commutator | C4 | C22×C3×C4 |
| Frattini, cosocle | C2×C4 | C23×C3 |
| prime radical | C2×C3×#41 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C22×C3×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×M16 | C2 | semidirect |
| 3. C2×C3×C4⋊C4 | C2 | semidirect |
| 4. C3×#103 | C2 | semidirect |
| 5. C3×#102 | C2 | semidirect |
| 6. #417 | C3 | direct (N × H) |
| 8. C3×#41 | C4 | semidirect |
| 20. C2×M16 | C2×C3 | semidirect |
| 21. C2×C4⋊C4 | C2×C3 | semidirect |
| 22. #103 | C2×C3 | semidirect |
| 23. #102 | C2×C3 | semidirect |
| 27. C3×Q8 | C2×C4 | semidirect |
| 30. C3×D4 | C2×C4 | semidirect |
| 41. #41 | C3×C4 | semidirect |
| 67. Q8 | C2×C3×C4 | semidirect |
| 70. D4 | C2×C3×C4 | semidirect |
| 97. C3 | #417 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#41 | 2 |
| C2×C3×M16 | 2 |
| C2×C3×C4⋊C4 | 2 |
| C3×#103 | 2 |
| C3×#102 | 2 |
| #417 | 3 |