Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 3. Q8×#10623494 | C2 | semidirect |
| 4. #19151348 | C2 | semidirect |
| 5. #19151344 | C2 | semidirect |
| 7. #475×C89 | C2 | semidirect |
| 46. Q8×C89 | SD16 | semidirect |
| 62. #10623494 | SD16 | semidirect |
| 80. C89 | #1666 | semidirect |
| 82. #475 | D89 | semidirect |
| 126. Q8 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19151972 | 2 |
| #19151798 | 2 |
| Q8×#10623494 | 2 |
| #19151348 | 2 |
| #19151344 | 2 |
| #19151341 | 2 |
| #475×C89 | 2 |
| #1666 | 89 |