Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
582 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 149 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×C42×D89 | C2 | semidirect |
| 2. #19151486 | C2 | semidirect |
| 3. #19151479 | C2 | semidirect |
| 5. #19151469 | C2 | semidirect |
| 6. #19151466 | C2 | semidirect |
| 7. C2×#126×C89 | C2 | semidirect |
| 40. C42×C89 | D4 | semidirect |
| 71. C2×D89 | #126 | semidirect |
| 83. C89 | #2852 | semidirect |
| 84. C2×#126 | D89 | semidirect |
| 123. C42 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D89 | 2 |
| #19151486 | 2 |
| #19151479 | 2 |
| #19151474 | 2 |
| #19151469 | 2 |
| #19151466 | 2 |
| C2×#126×C89 | 2 |
| #2852 | 89 |