Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
392 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D3 |
| commutator, socle | C22×C3 | C23×C4 |
| Fitting | C3×#423 | C2 |
| prime radical | C23×D3 | C2×C4 |
| cosocle | C2×C3×C4 | C24 |
| hypercenter | #423 | D3 |
| hypocenter | C3 | #2921 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C4 ◁ #423 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#423 | C2 | semidirect |
| 4. Dic3×M16 | C2 | semidirect |
| 5. #4924 | C2 | semidirect |
| 6. #4840 | C2 | semidirect |
| 17. C3×C4⋊C8 | C22 | semidirect |
| 19. #815 | C22 | semidirect |
| 20. C8×Dic3 | C22 | semidirect |
| 21. C4⋊(C3⋊C8) | C22 | semidirect |
| 25. #423 | D3 | semidirect |
| 57. C4⋊C8 | C2×D3 | semidirect |
| 146. C3 | #2921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#872 | 2 |
| C3×#423 | 2 |
| #5126 | 2 |
| Dic3×M16 | 2 |
| #4924 | 2 |
| #4840 | 2 |
| #2921 | 3 |