Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×#67 |
| commutator, cosocle | C2×C3×C4 | C24 |
| Frattini | C2×C4 | C23×D3 |
| Fitting | C3×#535 | C2 |
| socle | C22×C3 | C22×D4 |
| hypercenter | #535 | D3 |
| hypocenter | C3 | #3058 |
| LCS | G ▷ C2×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C2×#41 ◁ #535 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#535 | C2 | semidirect |
| 2. #5830 | C2 | semidirect |
| 3. C2×#948 | C2 | semidirect |
| 4. C22×#213 | C2 | semidirect |
| 5. #5215 | C2 | semidirect |
| 6. #5039 | C2 | semidirect |
| 7. #5038 | C2 | semidirect |
| 8. #5001 | C2 | semidirect |
| 9. #4998 | C2 | semidirect |
| 16. C3×#121 | C22 | semidirect |
| 26. #930 | C22 | semidirect |
| 29. C2×#208 | C22 | semidirect |
| 31. C22×C3⋊C8 | C22 | semidirect |
| 32. #832 | C22 | semidirect |
| 33. #809 | C22 | semidirect |
| 34. #808 | C22 | semidirect |
| 35. #807 | C22 | semidirect |
| 39. #535 | D3 | semidirect |
| 77. C2×C3⋊C8 | D4 | semidirect |
| 97. #121 | C2×D3 | semidirect |
| 244. C3 | #3058 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#535 | 2 |
| #5830 | 2 |
| C2×#948 | 2 |
| C22×#213 | 2 |
| #5215 | 2 |
| #5039 | 2 |
| #5038 | 2 |
| #5001 | 2 |
| #4998 | 2 |
| #3058 | 3 |