Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
1000 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 1000 conjugacy classes of subgroups — too many to draw. Only its 157 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 | #390×C89 | C2 |
| hypercenter | #390 | D89 |
| hypocenter | C89 | #2679 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15667982 | C2 | semidirect |
| 2. C2×#15667980 | C2 | semidirect |
| 3. #19151515 | C2 | semidirect |
| 4. #19151514 | C2 | semidirect |
| 5. #19151500 | C2 | semidirect |
| 6. #390×C89 | C2 | semidirect |
| 7. C24×D89 | C22 | semidirect |
| 13. C2×C4⋊Dic89 | C22 | semidirect |
| 14. C2×C22⋊Dic89 | C22 | semidirect |
| 15. C2×#13083551 | C22 | semidirect |
| 16. C2×#13083551 | C22 | semidirect |
| 17. C2×#13083551 | C22 | semidirect |
| 18. #15667919 | C22 | semidirect |
| 20. C2×C4⋊C4×C89 | C22 | semidirect |
| 21. C2×C22⋊C4×C89 | C22 | semidirect |
| 22. C2×C42×C89 | C22 | semidirect |
| 33. C2×D356 | D4 | semidirect |
| 46. C2×D4×C89 | D4 | semidirect |
| 116. C89 | #2679 | semidirect |
| 122. #390 | D89 | semidirect |
| 131. C2×C4⋊C4 | C2×D89 | semidirect |
| 136. C2×C22⋊C4 | C2×D89 | semidirect |
| 137. C2×C42 | C2×D89 | semidirect |
| 156. C2×D4 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667982 | 2 |
| C2×#15667980 | 2 |
| #19151515 | 2 |
| #19151514 | 2 |
| #19151500 | 2 |
| #390×C89 | 2 |
| #2679 | 89 |