Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
796 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 796 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, Frattini | C23 | C23×D3 |
| commutator, socle, cosocle | C23×C3 | C24 |
| Fitting | C3×#393 | C2 |
| hypercenter | #393 | D3 |
| hypocenter | C3 | #2670 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #393 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#947 | C2 | semidirect |
| 2. C2×#882 | C2 | semidirect |
| 3. C3×#393 | C2 | semidirect |
| 4. #4960 | C2 | semidirect |
| 5. #4957 | C2 | semidirect |
| 6. #4955 | C2 | semidirect |
| 7. #4672 | C2 | semidirect |
| 8. #4671 | C2 | semidirect |
| 9. #4669 | C2 | semidirect |
| 12. C22×C3×Q8 | C22 | semidirect |
| 16. C22×D12 | C22 | semidirect |
| 25. C2×(C2×D3)⋊C4 | C22 | semidirect |
| 26. C2×(C2×D3)⋊C4 | C22 | semidirect |
| 27. C2×(C2×D3)⋊C4 | C22 | semidirect |
| 28. C2×Dic3⋊C4 | C22 | semidirect |
| 29. C2×C4×Dic3 | C22 | semidirect |
| 31. C3×#95 | C22 | semidirect |
| 32. C3×#95 | C22 | semidirect |
| 33. C3⋊#95 | C22 | semidirect |
| 37. #393 | D3 | semidirect |
| 79. (C2×D3)⋊C4 | D4 | semidirect |
| 83. C22×Q8 | C2×D3 | semidirect |
| 103. #95 | C2×D3 | semidirect |
| 104. #95 | C2×D3 | semidirect |
| 306. C3 | #2670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#947 | 2 |
| C2×#882 | 2 |
| C3×#393 | 2 |
| #4960 | 2 |
| #4957 | 2 |
| #4955 | 2 |
| #4672 | 2 |
| #4671 | 2 |
| #4669 | 2 |
| #2670 | 3 |