Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15668060 | C2 | semidirect |
| 2. C2×#15668040 | C2 | semidirect |
| 3. C22×#13083561 | C2 | semidirect |
| 4. #19152167 | C2 | semidirect |
| 5. #19151746 | C2 | semidirect |
| 6. #19151738 | C2 | semidirect |
| 7. #19151592 | C2 | semidirect |
| 8. #19151566 | C2 | semidirect |
| 9. #419×C89 | C2 | semidirect |
| 13. C2×#13083575 | C22 | semidirect |
| 18. C2×Q8×D89 | C22 | semidirect |
| 30. #15667935 | C22 | semidirect |
| 31. #15667932 | C22 | semidirect |
| 32. #15667924 | C22 | semidirect |
| 36. #103×C89 | C22 | semidirect |
| 45. #13083574 | D4 | semidirect |
| 74. C2×Q8×C89 | D4 | semidirect |
| 146. C89 | #3010 | semidirect |
| 153. #419 | D89 | semidirect |
| 180. #103 | C2×D89 | semidirect |
| 200. C2×Q8 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668060 | 2 |
| C2×#15668040 | 2 |
| C22×#13083561 | 2 |
| #19152167 | 2 |
| #19151746 | 2 |
| #19151738 | 2 |
| #19151592 | 2 |
| #19151566 | 2 |
| #419×C89 | 2 |
| #3010 | 89 |