Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
308 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#6899⋊C2 |
| commutator, cosocle | C2×C92 | C22×C3 |
| Frattini, socle | C2×C32 | C2×C3×C3⋊D3 |
| Fitting | C22×#6899 | C2 |
| hypercenter | C22 | #6899⋊C2 |
| hypocenter | C92 | C3×D4 |
| LCS | G ▷ C2×C92 ▷ C92 | |
| UCS | C1 ◁ C2 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#6899 | C2 | semidirect |
| 2. C2×#6899⋊C2 | C2 | semidirect |
| 3. #6899⋊C4 | C2 | semidirect |
| 5. #10619673 | C3 | semidirect |
| 16. C22×C92 | C2×C3 | semidirect |
| 17. C2×C9⋊D9 | C2×C3 | semidirect |
| 19. C9⋊Dic9 | C2×C3 | semidirect |
| 21. #6899 | D4 | semidirect |
| 57. C92 | C3×D4 | semidirect |
| 151. C22 | #6899⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6899 | 2 |
| C2×#6899⋊C2 | 2 |
| #6899⋊C4 | 2 |
| #10619980 | 3 |
| #10619673 | 3 |
| #10619630 | 3 |