Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
836 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 173 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×#13083573 | C2 |
| hypercenter | #390 | D89 |
| hypocenter | C89 | #2432 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#15668012 | C2 | semidirect |
| 3. C2×#15667999 | C2 | semidirect |
| 4. C2×#15667992 | C2 | semidirect |
| 5. #19151514 | C2 | semidirect |
| 6. #19151503 | C2 | semidirect |
| 7. #19151473 | C2 | semidirect |
| 8. C4×#13083551 | C2 | semidirect |
| 9. #390×C89 | C2 | semidirect |
| 89. C2×C4×C89 | #41 | semidirect |
| 137. C89 | #2432 | semidirect |
| 144. #390 | D89 | semidirect |
| 243. C2×C4 | #13083573 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083573 | 2 |
| C2×#15668012 | 2 |
| C2×#15667999 | 2 |
| C2×#15667992 | 2 |
| #19151514 | 2 |
| #19151503 | 2 |
| #19151473 | 2 |
| C4×#13083551 | 2 |
| #390×C89 | 2 |
| #2432 | 89 |