Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
342 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92308⋊C2 |
| commutator, cosocle, hypocenter | #6896 | C23 |
| Frattini | C32 | C2×#1113 |
| Fitting | C2×#6896 | C22 |
| socle | C2×C32 | #1113 |
| LCS | G ▷ #6896 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#92309 | C2 | semidirect |
| 2. C2×#92308 | C2 | semidirect |
| 3. #92308⋊C2 | C2 | direct (N × H) |
| 6. C2×#6896 | C22 | semidirect |
| 7. #92309 | C22 | semidirect |
| 8. #92308 | C22 | semidirect |
| 11. C2×C9⋊D9 | D3 | semidirect |
| 18. #6896 | C23 | semidirect |
| 26. C2×C92 | C2×D3 | semidirect |
| 28. C9⋊D9 | C2×D3 | semidirect |
| 47. C92 | C22×D3 | semidirect |
| 138. C2 | #92308⋊C2 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92309 | 2 |
| C2×#92308 | 2 |
| #92308⋊C2 | 2 |
| C2×((C3⋊D3)⋊C9)⋊C2 | 3 |
| C2×D92 | 3 |