Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
552 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 153 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×#15668045 | C2 | semidirect |
| 2. C2×#15668043 | C2 | semidirect |
| 3. C2×#15668042 | C2 | semidirect |
| 5. C2×#15668010 | C2 | semidirect |
| 6. #19151991 | C2 | semidirect |
| 7. #19151989 | C2 | semidirect |
| 8. #19151976 | C2 | semidirect |
| 9. #19151969 | C2 | semidirect |
| 10. M16×Dic89 | C2 | semidirect |
| 11. C2×#137×C89 | C2 | semidirect |
| 62. #13083558 | D4 | semidirect |
| 86. M16×C89 | D4 | semidirect |
| 140. Dic89 | #137 | semidirect |
| 147. C89 | #3152 | semidirect |
| 151. C2×#137 | D89 | semidirect |
| 224. M16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668045 | 2 |
| C2×#15668043 | 2 |
| C2×#15668042 | 2 |
| #19152144 | 2 |
| C2×#15668010 | 2 |
| #19151991 | 2 |
| #19151989 | 2 |
| #19151976 | 2 |
| #19151969 | 2 |
| M16×Dic89 | 2 |
| C2×#137×C89 | 2 |
| #3152 | 89 |