Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 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. C4⋊Q8×D89 | C2 | semidirect |
| 3. #19151893 | C2 | semidirect |
| 4. #19151889 | C2 | semidirect |
| 5. #19151885 | C2 | semidirect |
| 6. #19151881 | C2 | semidirect |
| 7. #19151877 | C2 | semidirect |
| 8. #19151639 | C2 | semidirect |
| 9. #19151620 | C2 | semidirect |
| 11. #477×C89 | C2 | semidirect |
| 44. #13083575 | Q8 | semidirect |
| 86. Q8×C89 | C2×Q8 | semidirect |
| 100. D356 | C2×Q8 | semidirect |
| 138. C89 | #3079 | semidirect |
| 142. #477 | D89 | semidirect |
| 226. Q8 | Q8×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D89 | 2 |
| C4×#13083575 | 2 |
| #19151893 | 2 |
| #19151889 | 2 |
| #19151885 | 2 |
| #19151881 | 2 |
| #19151877 | 2 |
| #19151639 | 2 |
| #19151620 | 2 |
| #19151598 | 2 |
| #477×C89 | 2 |
| #3079 | 89 |