Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
452 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 137 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. #19152396 | C2 | semidirect |
| 2. C2×#15668018 | C2 | semidirect |
| 3. #19151870 | C2 | semidirect |
| 4. #19151865 | C2 | semidirect |
| 5. #19151858 | C2 | semidirect |
| 6. C2×#15667948 | C2 | semidirect |
| 7. #19151582 | C2 | semidirect |
| 8. C2×#135×C89 | C2 | semidirect |
| 23. #15667948 | C22 | semidirect |
| 24. #15667948 | C22 | semidirect |
| 25. #15667931 | C22 | semidirect |
| 26. #15667929 | C22 | semidirect |
| 32. C2×Q16×C89 | C22 | semidirect |
| 33. C2×SD16×C89 | C22 | semidirect |
| 34. C2×D8×C89 | C22 | semidirect |
| 133. C89 | #3067 | semidirect |
| 135. C2×#135 | D89 | semidirect |
| 153. C2×Q16 | C2×D89 | semidirect |
| 154. C2×SD16 | C2×D89 | semidirect |
| 155. C2×D8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152396 | 2 |
| C2×#15668018 | 2 |
| #19151870 | 2 |
| #19151865 | 2 |
| #19151858 | 2 |
| C2×#15667948 | 2 |
| #19151582 | 2 |
| C2×#135×C89 | 2 |
| #3067 | 89 |