Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
582 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 145 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 | #376×C89 | C2 |
| prime radical | #19151508 | C2 |
| hypercenter | #376 | D89 |
| hypocenter | C89 | #2603 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15668006 | C2 | semidirect |
| 2. C2×C4×D356 | C2 | semidirect |
| 3. #19151530 | C2 | semidirect |
| 4. #19151525 | C2 | semidirect |
| 5. #19151516 | C2 | semidirect |
| 7. #19151500 | C2 | semidirect |
| 8. #19151489 | C2 | semidirect |
| 9. #19151476 | C2 | semidirect |
| 10. #19151472 | C2 | semidirect |
| 11. #376×C89 | C2 | semidirect |
| 70. C42×C89 | D4 | semidirect |
| 144. C89 | #2603 | semidirect |
| 155. #376 | D89 | semidirect |
| 214. C42 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668006 | 2 |
| C2×C4×D356 | 2 |
| #19151530 | 2 |
| #19151525 | 2 |
| #19151516 | 2 |
| #19151508 | 2 |
| #19151500 | 2 |
| #19151489 | 2 |
| #19151476 | 2 |
| #19151472 | 2 |
| #376×C89 | 2 |
| #2603 | 89 |