Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
736 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 161 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×#15668037 | C2 | semidirect |
| 2. #19152162 | C2 | semidirect |
| 3. #19151771 | C2 | semidirect |
| 4. #19151766 | C2 | semidirect |
| 5. #19151615 | C2 | semidirect |
| 6. #19151582 | C2 | semidirect |
| 7. #585×C89 | C2 | semidirect |
| 8. C22×D356 | C22 | semidirect |
| 10. #15668037 | C22 | semidirect |
| 13. C2×#13083558 | C22 | semidirect |
| 14. #15668008 | C22 | semidirect |
| 15. #15668001 | C22 | semidirect |
| 18. #15667971 | C22 | semidirect |
| 19. #15667939 | C22 | semidirect |
| 20. #15667931 | C22 | semidirect |
| 21. #15667929 | C22 | semidirect |
| 23. 2−1+4×C89 | C22 | semidirect |
| 26. H(5,𝔽2)×C89 | C22 | semidirect |
| 56. #41×C89 | D4 | semidirect |
| 60. C2×Q8×C89 | D4 | semidirect |
| 68. C2×D4×C89 | D4 | semidirect |
| 135. C89 | #3021 | semidirect |
| 136. #585 | D89 | semidirect |
| 144. 2−1+4 | C2×D89 | semidirect |
| 147. H(5,𝔽2) | C2×D89 | semidirect |
| 177. #41 | C22⋊D89 | semidirect |
| 181. C2×Q8 | C22⋊D89 | semidirect |
| 194. C2×D4 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668037 | 2 |
| #19152162 | 2 |
| #19151771 | 2 |
| #19151766 | 2 |
| #19151615 | 2 |
| #19151582 | 2 |
| #585×C89 | 2 |
| #3021 | 89 |