Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
162 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 60 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 | C3×C42 |
| Frattini, cosocle | C2×#41 | C22×C3 |
| socle | C2×C3 | #342 |
| prime radical | C2×C3×#41 | C22 |
| 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 |
|---|---|---|
| 4. #1395 | C3 | direct (N × H) |
| 7. C2×C3×M16 | C4 | semidirect |
| 8. C22×C3×C8 | C4 | semidirect |
| 10. C3×#101 | C4 | semidirect |
| 40. C2×M16 | C3×C4 | semidirect |
| 41. C22×C8 | C3×C4 | semidirect |
| 43. #101 | C3×C4 | semidirect |
| 141. C3 | #1395 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#413 | 2 |
| C3×#410 | 2 |
| C3×#408 | 2 |
| #1395 | 3 |