Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
676 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 185 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 |
| prime radical | C22×D4×C89 | C22 |
| hypercenter | #390 | D89 |
| hypocenter | C89 | #2542 |
| 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×#15668011 | C2 | semidirect |
| 2. C2×#15667989 | C2 | semidirect |
| 4. #19151534 | C2 | semidirect |
| 6. #19151468 | C2 | semidirect |
| 7. #19151467 | C2 | semidirect |
| 8. C4×#13083553 | C2 | semidirect |
| 44. #13083553 | D4 | semidirect |
| 52. C2×D4×C89 | Q8 | semidirect |
| 99. C4×C89 | C22⋊Q8 | semidirect |
| 112. C89 | #2542 | semidirect |
| 147. C2×D4 | Dic178 | semidirect |
| 216. C4 | #15667989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668011 | 2 |
| C2×#15667989 | 2 |
| C2×D4×Dic89 | 2 |
| #19151534 | 2 |
| #19151501 | 2 |
| #19151468 | 2 |
| #19151467 | 2 |
| C4×#13083553 | 2 |
| #390×C89 | 2 |
| #2542 | 89 |