Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
422 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 161 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×#433 | C2 |
| prime radical | #5524 | C2 |
| cosocle | C2×C3×C4 | C24 |
| hypercenter | #433 | D3 |
| hypocenter | C3 | #2977 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C4 ◁ #433 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#433 | C2 | semidirect |
| 3. #5000 | C2 | semidirect |
| 4. #4836 | C2 | semidirect |
| 5. #4834 | C2 | semidirect |
| 6. #4727 | C2 | semidirect |
| 7. D3×C22⋊C8 | C2 | semidirect |
| 8. #4706 | C2 | semidirect |
| 9. C8×D12 | C2 | semidirect |
| 14. C2×ΓL(1,𝔽25) | C22 | semidirect |
| 17. C2×D3×C8 | C22 | semidirect |
| 24. C3×C4⋊C8 | C22 | semidirect |
| 26. C3×#97 | C22 | semidirect |
| 27. C3×C4×C8 | C22 | semidirect |
| 31. (C2×D3)⋊C8 | C22 | semidirect |
| 32. (C2×D3)⋊C8 | C22 | semidirect |
| 33. C4⋊(C3⋊C8) | C22 | semidirect |
| 34. #803 | C22 | semidirect |
| 35. C4×C3⋊C8 | C22 | semidirect |
| 42. #433 | D3 | semidirect |
| 90. C4⋊C8 | C2×D3 | semidirect |
| 98. #97 | C2×D3 | semidirect |
| 100. C4×C8 | C2×D3 | semidirect |
| 223. C3 | #2977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5524 | 2 |
| C3×#433 | 2 |
| #5000 | 2 |
| #4836 | 2 |
| #4834 | 2 |
| #4727 | 2 |
| D3×C22⋊C8 | 2 |
| #4706 | 2 |
| C8×D12 | 2 |
| #2977 | 3 |