Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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×#15668034 | C2 | semidirect |
| 2. C2×#15668032 | C2 | semidirect |
| 3. #19152144 | C2 | semidirect |
| 4. #19151991 | C2 | semidirect |
| 5. #19151989 | C2 | semidirect |
| 6. #19151986 | C2 | semidirect |
| 7. #19151984 | C2 | semidirect |
| 8. C2×#15667922 | C2 | semidirect |
| 9. C2×#135×C89 | C2 | semidirect |
| 51. C2×#10623494 | D4 | semidirect |
| 68. C2×C8×C89 | D4 | semidirect |
| 117. C89 | #3150 | semidirect |
| 120. C2×#135 | D89 | semidirect |
| 180. C2×C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668034 | 2 |
| C2×#15668032 | 2 |
| #19152144 | 2 |
| #19151991 | 2 |
| #19151989 | 2 |
| #19151986 | 2 |
| #19151984 | 2 |
| C2×#15667922 | 2 |
| C2×#135×C89 | 2 |
| #3150 | 89 |