Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
286 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 112 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 | #120 |
| commutator | C2×C4 | C22×C3×C4 |
| Frattini, cosocle | C22×C4 | C23×C3 |
| prime radical | C2×C3×#41 | C22 |
| 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 |
|---|---|---|
| 2. C3×#428 | C2 | semidirect |
| 5. C3×#382 | C2 | semidirect |
| 6. C3×#343 | C2 | semidirect |
| 7. C3×#339 | C2 | semidirect |
| 8. #1860 | C3 | direct (N × H) |
| 23. C3×#104 | C4 | semidirect |
| 28. #428 | C2×C3 | semidirect |
| 31. #382 | C2×C3 | semidirect |
| 32. #343 | C2×C3 | semidirect |
| 33. #339 | C2×C3 | semidirect |
| 50. C3×M16 | C2×C4 | semidirect |
| 65. C3×C42 | C2×C4 | semidirect |
| 80. #104 | C3×C4 | semidirect |
| 129. M16 | C2×C3×C4 | semidirect |
| 144. C42 | C2×C3×C4 | semidirect |
| 216. C3 | #1860 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#520 | 2 |
| C3×#428 | 2 |
| C2×C3×#104 | 2 |
| C3×#417 | 2 |
| C3×#382 | 2 |
| C3×#343 | 2 |
| C3×#339 | 2 |
| #1860 | 3 |