Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
548 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 125 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, socle, cosocle | C23×C89 | C24 |
| Fitting | #396×C89 | C2 |
| prime radical | C24×D89 | C22 |
| hypercenter | #396 | D89 |
| hypocenter | C89 | #2842 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #396 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19151535 | C2 | semidirect |
| 2. #19151533 | C2 | semidirect |
| 3. #19151522 | C2 | semidirect |
| 4. #19151521 | C2 | semidirect |
| 5. #19151520 | C2 | semidirect |
| 7. #396×C89 | C2 | semidirect |
| 9. C2×C4⋊Dic89 | C22 | semidirect |
| 10. C2×#13083553 | C22 | semidirect |
| 11. C2×#13083553 | C22 | semidirect |
| 17. #15667919 | C22 | semidirect |
| 18. C2×C4⋊C4×C89 | C22 | semidirect |
| 20. #95×C89 | C22 | semidirect |
| 90. C89 | #2842 | semidirect |
| 96. #396 | D89 | semidirect |
| 102. C2×C4⋊C4 | C2×D89 | semidirect |
| 110. #95 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19151535 | 2 |
| #19151533 | 2 |
| #19151522 | 2 |
| #19151521 | 2 |
| #19151520 | 2 |
| #19151453 | 2 |
| #396×C89 | 2 |
| #2842 | 89 |