Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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×D89 |
| commutator | C22×C89 | C23×C4 |
| Fitting | #379×C89 | C2 |
| socle, cosocle | C23×C89 | C24 |
| prime radical | C25×C89 | C22 |
| hypercenter | #379 | D89 |
| hypocenter | C89 | #2312 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #19151492 | C2 | semidirect |
| 3. #19151486 | C2 | semidirect |
| 4. #19151456 | C2 | semidirect |
| 6. C22⋊C4×Dic89 | C2 | semidirect |
| 10. C2×#13083553 | C22 | semidirect |
| 11. C2×C22⋊Dic89 | C4 | semidirect |
| 17. C2×C4×Dic89 | C22 | semidirect |
| 18. #15667919 | C22 | semidirect |
| 19. #15667919 | C22 | semidirect |
| 107. C89 | #2312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic89 | 2 |
| #19151492 | 2 |
| #19151486 | 2 |
| #19151456 | 2 |
| #19151454 | 2 |
| C22⋊C4×Dic89 | 2 |
| #379×C89 | 2 |
| #2312 | 89 |