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×#15668038 | C2 | semidirect |
| 2. C4×#13083574 | C2 | semidirect |
| 3. #19151795 | C2 | semidirect |
| 4. #19151790 | C2 | semidirect |
| 5. #19151622 | C2 | semidirect |
| 6. #19151603 | C2 | semidirect |
| 7. C2×#127×C89 | C2 | semidirect |
| 10. C2×#13083562 | C22 | semidirect |
| 11. C2×#13083559 | C22 | semidirect |
| 13. C4×Dic178 | C22 | semidirect |
| 14. C4×D356 | C22 | semidirect |
| 19. C4⋊#10623494 | C22 | semidirect |
| 20. #15667933 | C22 | semidirect |
| 28. #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 |
| 107. C2×#127 | D89 | semidirect |
| 201. C4 | #15668038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668038 | 2 |
| C4×#13083574 | 2 |
| #19151795 | 2 |
| #19151790 | 2 |
| #19151622 | 2 |
| #19151603 | 2 |
| C2×#127×C89 | 2 |
| #3038 | 89 |