Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
228 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 92 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 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C3×C4 |
| Frattini, cosocle | C22×C4 | C23×C3 |
| prime radical | C23×C3 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #1506 | C3 | direct (N × H) |
| 6. C3×C4⋊Q8 | C4 | semidirect |
| 7. C3×C4⋊Q8 | C4 | semidirect |
| 12. C3×C4×Q8 | C4 | semidirect |
| 45. C4⋊Q8 | C3×C4 | semidirect |
| 46. C4⋊Q8 | C3×C4 | semidirect |
| 51. C4×Q8 | C3×C4 | semidirect |
| 146. C3 | #1506 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#533 | 2 |
| C3×#432 | 2 |
| C3×#376 | 2 |
| C3×#328 | 2 |
| #1506 | 3 |