Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
688 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15667995 | C2 | semidirect |
| 3. #19151500 | C2 | semidirect |
| 4. #19151496 | C2 | semidirect |
| 5. #19151489 | C2 | semidirect |
| 6. #19151477 | C2 | semidirect |
| 7. #19151458 | C2 | semidirect |
| 8. C22×C42×C89 | C2 | semidirect |
| 50. C22×C4×C89 | D4 | semidirect |
| 107. C4×C89 | #123 | semidirect |
| 118. C89 | #2854 | semidirect |
| 121. C22×C42 | D89 | semidirect |
| 160. C22×C4 | D356 | semidirect |
| 227. C4 | #15667995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667995 | 2 |
| C2×#15667986 | 2 |
| #19151500 | 2 |
| #19151496 | 2 |
| #19151489 | 2 |
| #19151477 | 2 |
| #19151458 | 2 |
| C22×C42×C89 | 2 |
| #2854 | 89 |