Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
708 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 169 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 | #384×C89 | C2 |
| prime radical | C2×#15667987 | C2 |
| hypercenter | #384 | D89 |
| hypocenter | C89 | #2501 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15667997 | C2 | semidirect |
| 3. C2×C4⋊C4×D89 | C2 | semidirect |
| 4. #19151533 | C2 | semidirect |
| 5. #19151500 | C2 | semidirect |
| 6. #19151499 | C2 | semidirect |
| 7. #19151467 | C2 | semidirect |
| 8. C4×#13083551 | C2 | semidirect |
| 9. #384×C89 | C2 | semidirect |
| 51. #13083551 | D4 | semidirect |
| 112. C4×C89 | #123 | semidirect |
| 124. C89 | #2501 | semidirect |
| 132. #384 | D89 | semidirect |
| 239. C4 | #15667997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667997 | 2 |
| C2×#15667987 | 2 |
| C2×C4⋊C4×D89 | 2 |
| #19151533 | 2 |
| #19151500 | 2 |
| #19151499 | 2 |
| #19151467 | 2 |
| C4×#13083551 | 2 |
| #384×C89 | 2 |
| #2501 | 89 |