Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
528 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 221 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. #19152073 | C2 | semidirect |
| 2. #19151710 | C2 | semidirect |
| 3. D8×Dic89 | C2 | semidirect |
| 4. #19151636 | C2 | semidirect |
| 5. #19151603 | C2 | semidirect |
| 6. #19151553 | C2 | semidirect |
| 10. D4×Dic89 | C22 | semidirect |
| 14. #15667946 | C22 | semidirect |
| 15. #15667944 | C22 | semidirect |
| 16. #15667933 | C22 | semidirect |
| 17. #15667922 | C22 | semidirect |
| 18. C8×Dic89 | C22 | semidirect |
| 20. C2×D8×C89 | C4 | semidirect |
| 37. C2×D4×C89 | C2×C4 | semidirect |
| 40. D8×C89 | C2×C4 | semidirect |
| 41. D8×C89 | C2×C4 | semidirect |
| 42. C2×C8×C89 | C2×C4 | semidirect |
| 78. C89 | #2948 | semidirect |
| 87. C2×D8 | Dic89 | semidirect |
| 105. C2×D4 | C2×Dic89 | semidirect |
| 109. D8 | C2×Dic89 | semidirect |
| 110. D8 | C2×Dic89 | semidirect |
| 113. C2×C8 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152073 | 2 |
| #19151710 | 2 |
| D8×Dic89 | 2 |
| #19151636 | 2 |
| #19151603 | 2 |
| #19151553 | 2 |
| C22×D8×C89 | 2 |
| #2948 | 89 |