Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
464 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 117 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 | #399×C89 | C2 |
| prime radical | #19151507 | C2 |
| hypercenter | #399 | D89 |
| hypocenter | C89 | #2826 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #399 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19151537 | C2 | semidirect |
| 2. #19151527 | C2 | semidirect |
| 3. #19151520 | C2 | semidirect |
| 4. #19151515 | C2 | semidirect |
| 5. #19151514 | C2 | semidirect |
| 7. #19151475 | C2 | semidirect |
| 8. #19151470 | C2 | semidirect |
| 9. #399×C89 | C2 | semidirect |
| 126. C89 | #2826 | semidirect |
| 128. #399 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19151537 | 2 |
| #19151527 | 2 |
| #19151520 | 2 |
| #19151515 | 2 |
| #19151514 | 2 |
| #19151507 | 2 |
| #19151475 | 2 |
| #19151470 | 2 |
| #399×C89 | 2 |
| #2826 | 89 |