Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
204 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | #397 |
| commutator, Frattini, cosocle | C22×C4 | C23×C3 |
| prime radical | C22×C3×D4 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3 ◁ C22×C3×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#430 | C2 | semidirect |
| 5. C3×#344 | C2 | semidirect |
| 6. C3×#344 | C2 | semidirect |
| 7. C3×H(3,ℤ/4) | C2 | semidirect |
| 8. #2081 | C3 | direct (N × H) |
| 20. #430 | C2×C3 | semidirect |
| 24. #344 | C2×C3 | semidirect |
| 25. #344 | C2×C3 | semidirect |
| 26. H(3,ℤ/4) | C2×C3 | semidirect |
| 165. C3 | #2081 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#430 | 2 |
| C3×#418 | 2 |
| C2×C3×#100 | 2 |
| C3×#344 | 2 |
| C3×H(3,ℤ/4) | 2 |
| #2081 | 3 |