Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×Q16×D89 | C2 | semidirect |
| 3. #19151976 | C2 | semidirect |
| 4. #19151839 | C2 | semidirect |
| 5. #19151836 | C2 | semidirect |
| 6. #19151806 | C2 | semidirect |
| 7. #19151754 | C2 | semidirect |
| 8. #19151752 | C2 | semidirect |
| 9. Q16×Dic89 | C2 | semidirect |
| 11. C22×Q16×C89 | C2 | semidirect |
| 76. Q16×C89 | D4 | semidirect |
| 94. C22⋊D89 | Q16 | direct (N × H) |
| 112. C22×C89 | C2×Q16 | semidirect |
| 116. C2×D89 | C2×Q16 | semidirect |
| 126. Dic89 | C2×Q16 | semidirect |
| 133. C89 | D4×Q16 | semidirect |
| 135. C22×Q16 | D89 | semidirect |
| 193. Q16 | C22⋊D89 | direct (N × H) |
| 248. C22 | Q16×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D89 | 2 |
| Q8×C22⋊D89 | 2 |
| #19151976 | 2 |
| #19151839 | 2 |
| #19151836 | 2 |
| #19151806 | 2 |
| #19151754 | 2 |
| #19151752 | 2 |
| Q16×Dic89 | 2 |
| C8×C22⋊D89 | 2 |
| C22×Q16×C89 | 2 |
| D4×Q16 | 89 |