Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
872 conjugacy classes of subgroups; only the 368 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 368 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3 | C24 |
| commutator | C22 | C23×C3×C4 |
| Frattini, cosocle | C23 | C24×C3 |
| prime radical | C22×C3×#41 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C3 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×C4×Q8 | C2 | semidirect |
| 3. C3×#390 | C2 | semidirect |
| 4. C3×#380 | C2 | semidirect |
| 5. C3×C4×C22⋊C4 | C2 | semidirect |
| 6. #2341 | C3 | direct (N × H) |
| 8. C2×C3×#41 | C4 | semidirect |
| 20. C2×C4×Q8 | C2×C3 | semidirect |
| 21. #390 | C2×C3 | semidirect |
| 22. #380 | C2×C3 | semidirect |
| 23. C4×C22⋊C4 | C2×C3 | semidirect |
| 41. C2×#41 | C3×C4 | semidirect |
| 58. C3×Q8 | C22⋊C4 | semidirect |
| 70. C2×C3×C4 | #41 | semidirect |
| 107. Q8 | C3×C22⋊C4 | semidirect |
| 119. C2×C4 | C3×#41 | semidirect |
| 140. C3 | #2341 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#41 | 2 |
| C2×C3×C4×Q8 | 2 |
| C3×#390 | 2 |
| C3×#380 | 2 |
| C3×C4×C22⋊C4 | 2 |
| #2341 | 3 |