Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
124 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 58 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, Frattini, cosocle | C2×C4 | C23×C3 |
| prime radical | C3×#121 | C2 |
| LCS | G ▷ C2×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 |
|---|---|---|
| 1. C2×C3×SD16 | C2 | semidirect |
| 2. C22×C3×C8 | C2 | semidirect |
| 3. C3×C22⋊Q8 | C2 | semidirect |
| 5. C3×#106 | C2 | semidirect |
| 6. C3×#103 | C2 | semidirect |
| 7. C3×#102 | C2 | semidirect |
| 8. #465 | C3 | direct (N × H) |
| 22. C2×SD16 | C2×C3 | semidirect |
| 23. C22×C8 | C2×C3 | semidirect |
| 24. C22⋊Q8 | C2×C3 | semidirect |
| 26. #106 | C2×C3 | semidirect |
| 27. #103 | C2×C3 | semidirect |
| 28. #102 | C2×C3 | semidirect |
| 44. C3×C8 | D4 | semidirect |
| 63. C22×C3 | SD16 | semidirect |
| 86. C8 | C3×D4 | semidirect |
| 97. C22 | C3×SD16 | semidirect |
| 105. C3 | #465 | 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 |
| C22×C3×C8 | 2 |
| C3×C22⋊Q8 | 2 |
| C3×#121 | 2 |
| C3×#106 | 2 |
| C3×#103 | 2 |
| C3×#102 | 2 |
| #465 | 3 |