Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
828 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 280 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C3 | C23 |
| commutator | C22 | C2×C3×C42 |
| Frattini, cosocle | C24 | C23×C3 |
| prime radical | C25×C3 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C3 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C3×C42 | C2 | semidirect |
| 3. C2×C3×#95 | C2 | semidirect |
| 4. #1437 | C3 | direct (N × H) |
| 10. C2×C3×C22⋊C4 | C4 | semidirect |
| 14. C22×C42 | C2×C3 | semidirect |
| 15. C2×#95 | C2×C3 | semidirect |
| 38. C2×C22⋊C4 | C3×C4 | semidirect |
| 51. C23×C3 | C42 | semidirect |
| 65. C2×C3×C4 | C22⋊C4 | semidirect |
| 110. C23 | C3×C42 | semidirect |
| 124. C2×C4 | C3×C22⋊C4 | semidirect |
| 147. C3 | #1437 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C22⋊C4 | 2 |
| C22×C3×C42 | 2 |
| C2×C3×#95 | 2 |
| #1437 | 3 |