Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
620 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 181 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 | C22×D356 | C22 |
| hypercenter | #384 | D89 |
| hypocenter | C89 | #2538 |
| 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×#15667992 | C2 | semidirect |
| 2. C2×C4×Dic178 | C2 | semidirect |
| 4. #19151520 | C2 | semidirect |
| 6. #19151497 | C2 | semidirect |
| 7. #19151455 | C2 | semidirect |
| 8. #384×C89 | C2 | semidirect |
| 31. C2×Dic178 | D4 | semidirect |
| 34. C2×D356 | Q8 | semidirect |
| 106. C4×C89 | C22⋊Q8 | semidirect |
| 119. C89 | #2538 | semidirect |
| 126. #384 | D89 | semidirect |
| 228. C4 | #15667992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667992 | 2 |
| C2×C4×Dic178 | 2 |
| C2×C4×D356 | 2 |
| #19151520 | 2 |
| #19151499 | 2 |
| #19151497 | 2 |
| #19151455 | 2 |
| #384×C89 | 2 |
| #2538 | 89 |