Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19152333 | C2 | semidirect |
| 2. D4×Dic178 | C2 | semidirect |
| 3. #19151959 | C2 | semidirect |
| 4. #19151945 | C2 | semidirect |
| 5. #19151887 | C2 | semidirect |
| 6. #19151883 | C2 | semidirect |
| 7. #19151815 | C2 | semidirect |
| 9. #19151728 | C2 | semidirect |
| 10. #19151707 | C2 | semidirect |
| 11. C4×SD16×C89 | C2 | semidirect |
| 125. C89 | #3373 | semidirect |
| 136. C4×SD16 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152333 | 2 |
| D4×Dic178 | 2 |
| #19151959 | 2 |
| #19151945 | 2 |
| #19151887 | 2 |
| #19151883 | 2 |
| #19151815 | 2 |
| #19151793 | 2 |
| #19151728 | 2 |
| #19151707 | 2 |
| C4×SD16×C89 | 2 |
| #3373 | 89 |