Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
804 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 804 conjugacy classes of subgroups — too many to draw. Only its 153 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 | #399×C89 | C2 |
| hypercenter | #399 | D89 |
| hypocenter | C89 | #2656 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #399 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15667987 | C2 | semidirect |
| 2. C2×#15667985 | C2 | semidirect |
| 3. #19151533 | C2 | semidirect |
| 4. #19151508 | C2 | semidirect |
| 5. #19151507 | C2 | semidirect |
| 6. #95×D89 | C2 | semidirect |
| 7. #399×C89 | C2 | semidirect |
| 34. C2×C4×D89 | D4 | semidirect |
| 92. C89 | #2656 | semidirect |
| 96. #399 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667987 | 2 |
| C2×#15667985 | 2 |
| #19151533 | 2 |
| #19151508 | 2 |
| #19151507 | 2 |
| #95×D89 | 2 |
| #399×C89 | 2 |
| #2656 | 89 |