Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 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×#15668040 | C2 | semidirect |
| 2. C2×#15668009 | C2 | semidirect |
| 3. C4×#13083574 | C2 | semidirect |
| 4. #19151799 | C2 | semidirect |
| 5. #19151794 | C2 | semidirect |
| 6. #19151604 | C2 | semidirect |
| 7. #423×C89 | C2 | semidirect |
| 12. C2×#13083563 | C22 | semidirect |
| 13. C2×D712 | C22 | semidirect |
| 17. C4×Dic178 | C22 | semidirect |
| 18. C4×D356 | C22 | semidirect |
| 23. #15667934 | C22 | semidirect |
| 26. C4⋊C8×C89 | C22 | semidirect |
| 29. #13083574 | D4 | semidirect |
| 78. D356 | C2×D4 | semidirect |
| 82. Dic178 | C2×D4 | semidirect |
| 94. C4×C89 | AGL(1,ℤ/8) | semidirect |
| 105. C89 | #3038 | semidirect |
| 111. #423 | D89 | semidirect |
| 130. C4⋊C8 | C2×D89 | semidirect |
| 201. C4 | #15668040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668040 | 2 |
| C2×#15668009 | 2 |
| C4×#13083574 | 2 |
| #19151799 | 2 |
| #19151794 | 2 |
| #19151604 | 2 |
| #423×C89 | 2 |
| #3038 | 89 |