Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
370 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 133 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. Q8×Dic178 | C2 | semidirect |
| 3. #19151995 | C2 | semidirect |
| 4. #19151994 | C2 | semidirect |
| 7. #19151881 | C2 | semidirect |
| 8. #19151722 | C2 | semidirect |
| 11. #475×C89 | C2 | semidirect |
| 49. #13083561 | Q8 | semidirect |
| 76. Q8×C89 | C2×Q8 | semidirect |
| 94. Dic178 | SD16 | semidirect |
| 97. #10623494 | C2×Q8 | semidirect |
| 118. C89 | Q8×SD16 | semidirect |
| 126. #475 | D89 | semidirect |
| 198. Q8 | Q8×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic178 | 2 |
| #19152263 | 2 |
| #19151995 | 2 |
| #19151994 | 2 |
| #19151889 | 2 |
| #19151887 | 2 |
| #19151881 | 2 |
| #19151722 | 2 |
| C4×#13083561 | 2 |
| #19151683 | 2 |
| #475×C89 | 2 |
| Q8×SD16 | 89 |