Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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. C22×Dic356 | C2 | semidirect |
| 2. C2×Q16×D89 | C2 | semidirect |
| 4. #19151976 | C2 | semidirect |
| 5. #19151840 | C2 | semidirect |
| 6. #19151807 | C2 | semidirect |
| 7. #19151755 | C2 | semidirect |
| 8. #19151753 | C2 | semidirect |
| 9. #19151692 | C2 | semidirect |
| 11. #467×C89 | C2 | semidirect |
| 55. Dic356 | D4 | semidirect |
| 90. C22⋊D89 | Q16 | semidirect |
| 112. C22×C89 | C2×Q16 | semidirect |
| 116. C2×D89 | C2×Q16 | semidirect |
| 126. Dic89 | C2×Q16 | semidirect |
| 133. C89 | D4×Q16 | semidirect |
| 139. #467 | D89 | semidirect |
| 248. C22 | Q16×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic356 | 2 |
| C2×Q16×D89 | 2 |
| #19152261 | 2 |
| #19151976 | 2 |
| #19151840 | 2 |
| #19151807 | 2 |
| #19151755 | 2 |
| #19151753 | 2 |
| #19151692 | 2 |
| C8×C22⋊D89 | 2 |
| #467×C89 | 2 |
| D4×Q16 | 89 |