Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
1058 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 1058 conjugacy classes of subgroups — too many to draw. Only its 451 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D89 |
| commutator, socle, cosocle | C22×C89 | C25 |
| Fitting | H(3,𝔽4)×C89 | C2 |
| hypercenter | H(3,𝔽4) | D89 |
| hypocenter | C89 | #3529 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19152348 | C2 | semidirect |
| 2. #19152342 | C2 | semidirect |
| 3. #19152337 | C2 | semidirect |
| 4. #19152147 | C2 | semidirect |
| 5. #19152127 | C2 | semidirect |
| 6. #19152104 | C2 | semidirect |
| 7. H(3,𝔽4)×C89 | C2 | semidirect |
| 8. C2×#13083575 | C22 | semidirect |
| 10. C23×Dic89 | C22 | semidirect |
| 11. #15668010 | C22 | semidirect |
| 13. #15668005 | C22 | semidirect |
| 14. #15668004 | C22 | semidirect |
| 15. #15668000 | C22 | semidirect |
| 16. #15667996 | C22 | semidirect |
| 17. #15667994 | C22 | semidirect |
| 19. #15667989 | C22 | semidirect |
| 20. #15667988 | C22 | semidirect |
| 21. #15667985 | C22 | semidirect |
| 24. #15667981 | C22 | semidirect |
| 25. Q8×Dic89 | C22 | semidirect |
| 27. #15667972 | C22 | semidirect |
| 28. #15667968 | C22 | semidirect |
| 29. C42×D89 | C22 | semidirect |
| 98. C89 | #3529 | semidirect |
| 101. H(3,𝔽4) | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152348 | 2 |
| #19152342 | 2 |
| #19152337 | 2 |
| #19152147 | 2 |
| #19152127 | 2 |
| #19152104 | 2 |
| H(3,𝔽4)×C89 | 2 |
| #3529 | 89 |