Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #19151614 | C2 | semidirect |
| 3. #19151594 | C2 | semidirect |
| 4. #19151592 | C2 | semidirect |
| 5. #19151571 | C2 | semidirect |
| 6. #19151566 | C2 | semidirect |
| 7. #421×C89 | C2 | semidirect |
| 10. #15668059 | C4 | semidirect |
| 12. #15668058 | C4 | semidirect |
| 20. C22×#10623494 | C22 | semidirect |
| 21. #15667971 | C22 | semidirect |
| 30. C2×M16×C89 | C22 | semidirect |
| 31. #117×C89 | C22 | semidirect |
| 167. C89 | #1794 | semidirect |
| 170. #421 | D89 | semidirect |
| 188. C2×M16 | C2×D89 | semidirect |
| 191. #117 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152434 | 2 |
| #19151614 | 2 |
| #19151594 | 2 |
| #19151592 | 2 |
| #19151571 | 2 |
| #19151566 | 2 |
| #421×C89 | 2 |
| #1794 | 89 |