Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
548 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D3 |
| commutator, socle, cosocle | C23×C3 | C24 |
| Fitting | C3×#399 | C2 |
| prime radical | C24×D3 | C22 |
| hypercenter | #399 | D3 |
| hypocenter | C3 | #2842 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #399 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#399 | C2 | semidirect |
| 2. #4994 | C2 | semidirect |
| 4. #4949 | C2 | semidirect |
| 5. #4676 | C2 | semidirect |
| 8. C2×C3×C4⋊C4 | C22 | semidirect |
| 13. C2×C4⋊Dic3 | C22 | semidirect |
| 14. C2×Dic3⋊C4 | C22 | semidirect |
| 15. C3×#95 | C22 | semidirect |
| 16. C3⋊#95 | C22 | semidirect |
| 18. #399 | D3 | semidirect |
| 40. C2×C4⋊C4 | C2×D3 | semidirect |
| 46. #95 | C2×D3 | semidirect |
| 127. C3 | #2842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#399 | 2 |
| #4994 | 2 |
| #4955 | 2 |
| #4949 | 2 |
| #4676 | 2 |
| #2842 | 3 |