Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
672 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 153 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 | C2×#117×C89 | C2 |
| prime radical | C24×D89 | C22 |
| hypercenter | C2×#117 | D89 |
| hypocenter | C89 | #2482 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C2×#117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #19151533 | C2 | semidirect |
| 3. #19151524 | C2 | semidirect |
| 4. #19151489 | C2 | semidirect |
| 5. #19151470 | C2 | semidirect |
| 6. #19151461 | C2 | semidirect |
| 8. C2×#117×C89 | C2 | semidirect |
| 11. C2×#13083553 | C22 | semidirect |
| 18. #15667919 | C22 | semidirect |
| 19. #15667919 | C22 | semidirect |
| 20. #15667919 | C22 | semidirect |
| 23. C2×C4⋊C4×C89 | C22 | semidirect |
| 24. C2×C4⋊C4×C89 | C22 | semidirect |
| 26. C2×C42×C89 | C22 | semidirect |
| 109. C89 | #2482 | semidirect |
| 110. C2×#117 | D89 | semidirect |
| 123. C2×C4⋊C4 | C2×D89 | semidirect |
| 124. C2×C4⋊C4 | C2×D89 | semidirect |
| 132. C2×C42 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083551 | 2 |
| #19151533 | 2 |
| #19151524 | 2 |
| #19151489 | 2 |
| #19151470 | 2 |
| #19151461 | 2 |
| #19151453 | 2 |
| C2×#117×C89 | 2 |
| #2482 | 89 |