Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1202 conjugacy classes of subgroups; only the 800 normal subgroups are shown.
This group has 1202 conjugacy classes of subgroups — too many to draw. Only its 800 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, Frattini, cosocle | C22 | C25×C3 |
| socle | C22×C3 | C25 |
| 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 |
|---|---|---|
| 1. C3×Q82 | C2 | semidirect |
| 2. C3×#555 | C2 | semidirect |
| 3. C3×#550 | C2 | semidirect |
| 4. C3×#532 | C2 | semidirect |
| 5. C3×C4×#41 | C2 | semidirect |
| 6. #3483 | C3 | direct (N × H) |
| 19. Q82 | C2×C3 | semidirect |
| 20. #555 | C2×C3 | semidirect |
| 21. #550 | C2×C3 | semidirect |
| 22. #532 | C2×C3 | semidirect |
| 23. C4×#41 | C2×C3 | semidirect |
| 52. C3×Q8 | #41 | semidirect |
| 84. Q8 | C3×#41 | semidirect |
| 103. C3 | #3483 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q82 | 2 |
| C3×#555 | 2 |
| C3×#550 | 2 |
| C3×#532 | 2 |
| C3×C4×#41 | 2 |
| #3483 | 3 |