Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
284 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 148 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C3×C8 | C22⋊C4 |
| commutator | C22 | C2×C3×C42 |
| Frattini, cosocle | C22×C4 | C23×C3 |
| socle | C2×C3 | C4×C22⋊C4 |
| prime radical | C2×C3×#41 | C22 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C3×C8 ◁ C22×C3×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C3×#405 | C2 | semidirect |
| 5. C3×#344 | C2 | semidirect |
| 6. #1757 | C3 | direct (N × H) |
| 10. C2×C3×M16 | C4 | semidirect |
| 13. C22×C3×C8 | C4 | semidirect |
| 16. C3×#101 | C4 | semidirect |
| 17. C3×#100 | C4 | semidirect |
| 24. #405 | C2×C3 | semidirect |
| 25. #344 | C2×C3 | semidirect |
| 51. C2×M16 | C3×C4 | semidirect |
| 54. C22×C8 | C3×C4 | semidirect |
| 57. #101 | C3×C4 | semidirect |
| 58. #100 | C3×C4 | semidirect |
| 144. C3 | #1757 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#131 | 2 |
| C3×#413 | 2 |
| C3×#410 | 2 |
| C3×#405 | 2 |
| C3×#344 | 2 |
| #1757 | 3 |