Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
232 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 64 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, Frattini, cosocle | C22×C4 | C23×C3 |
| prime radical | C3×#538 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ 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×#483 | C2 | semidirect |
| 3. C3×#480 | C2 | semidirect |
| 4. C3×#397 | C2 | semidirect |
| 5. C3×#328 | C2 | semidirect |
| 6. C3×#327 | C2 | semidirect |
| 7. C3×#323 | C2 | semidirect |
| 8. #1612 | C3 | direct (N × H) |
| 29. #483 | C2×C3 | semidirect |
| 30. #480 | C2×C3 | semidirect |
| 31. #397 | C2×C3 | semidirect |
| 32. #328 | C2×C3 | semidirect |
| 33. #327 | C2×C3 | semidirect |
| 34. #323 | C2×C3 | semidirect |
| 219. C3 | #1612 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#538 | 2 |
| C3×#483 | 2 |
| C3×#480 | 2 |
| C3×#397 | 2 |
| C3×#328 | 2 |
| C3×#327 | 2 |
| C3×#323 | 2 |
| #1612 | 3 |