Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
258 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C3×C4 | #99 |
| commutator | C2×C4 | C22×C3×C4 |
| Frattini, cosocle | C2×D4 | C23×C3 |
| socle | C2×C3 | C2×#99 |
| prime radical | C3×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C2×C3×#41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#410 | C2 | semidirect |
| 3. C3×#354 | C2 | semidirect |
| 4. C3×#353 | C2 | semidirect |
| 5. #2126 | C3 | direct (N × H) |
| 6. C2×C3×#41 | C4 | semidirect |
| 8. C3×C4⋊Q8 | C4 | semidirect |
| 10. C3×#124 | C4 | semidirect |
| 15. C2×C3×C42 | C4 | semidirect |
| 19. #410 | C2×C3 | semidirect |
| 20. #354 | C2×C3 | semidirect |
| 21. #353 | C2×C3 | semidirect |
| 46. C2×#41 | C3×C4 | semidirect |
| 48. C4⋊Q8 | C3×C4 | semidirect |
| 50. #124 | C3×C4 | semidirect |
| 55. C2×C42 | C3×C4 | semidirect |
| 165. C3 | #2126 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#532 | 2 |
| C3×#410 | 2 |
| C3×#354 | 2 |
| C3×#353 | 2 |
| #2126 | 3 |