Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
738 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 738 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15668043 | C2 | semidirect |
| 3. #19151754 | C2 | semidirect |
| 4. #19151737 | C2 | semidirect |
| 5. #19151607 | C2 | semidirect |
| 6. #19151562 | C2 | semidirect |
| 7. C23×Q8×C89 | C2 | semidirect |
| 10. C2×#13083564 | C22 | semidirect |
| 11. C2×#13083561 | C22 | semidirect |
| 19. #15667936 | C22 | semidirect |
| 51. C2×Q8×C89 | D4 | semidirect |
| 93. C22×C89 | #137 | semidirect |
| 109. C89 | #3004 | semidirect |
| 110. C23×Q8 | D89 | semidirect |
| 146. C2×Q8 | C22⋊D89 | semidirect |
| 204. C22 | #15668043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668043 | 2 |
| #19152109 | 2 |
| #19151754 | 2 |
| #19151737 | 2 |
| #19151607 | 2 |
| #19151562 | 2 |
| C23×Q8×C89 | 2 |
| #3004 | 89 |