Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
268 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 57 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×#6897⋊C2 |
| commutator, cosocle | C2×C92 | C22×C3 |
| Frattini, socle | C2×C32 | C2×C3×C3⋊D3 |
| Fitting | C22×#6897 | C2 |
| hypercenter | C22 | #6897⋊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×#6897 | C2 | semidirect |
| 2. C2×#6897⋊C2 | C2 | semidirect |
| 3. #11757614 | C2 | semidirect |
| 4. #10619673 | C3 | semidirect |
| 11. C22×C92 | C2×C3 | semidirect |
| 12. C2×C9⋊D9 | C2×C3 | semidirect |
| 14. C9⋊Dic9 | C2×C3 | semidirect |
| 16. #6897 | D4 | semidirect |
| 36. C92 | C3×D4 | semidirect |
| 92. C22 | #6897⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6897 | 2 |
| C2×#6897⋊C2 | 2 |
| #11757614 | 2 |
| #10619673 | 3 |
| #10619630 | 3 |