Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
452 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 268 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 | C24 |
| commutator | C22 | C23×C3×C4 |
| Frattini, cosocle | C2×C4 | C24×C3 |
| socle | C22×C3 | C23×C4 |
| prime radical | C22×C3×D4 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#436 | C2 | semidirect |
| 3. C3×#431 | C2 | semidirect |
| 4. C3×#407 | C2 | semidirect |
| 5. #2975 | C3 | direct (N × H) |
| 8. C2×C3×M16 | C22 | semidirect |
| 14. C3×C4⋊C8 | C22 | semidirect |
| 16. C3×C22⋊C8 | C22 | semidirect |
| 17. C3×C4×C8 | C22 | semidirect |
| 19. #436 | C2×C3 | semidirect |
| 20. #431 | C2×C3 | semidirect |
| 21. #407 | C2×C3 | semidirect |
| 40. C2×M16 | C22×C3 | semidirect |
| 46. C4⋊C8 | C22×C3 | semidirect |
| 48. C22⋊C8 | C22×C3 | semidirect |
| 49. C4×C8 | C22×C3 | semidirect |
| 61. C2×C3×C4 | M16 | semidirect |
| 108. C2×C4 | C3×M16 | semidirect |
| 133. C3 | #2975 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D4 | 2 |
| C3×#436 | 2 |
| C3×#431 | 2 |
| C3×#407 | 2 |
| #2975 | 3 |