Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
356 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 139 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. #19152001 | C2 | semidirect |
| 3. #19151933 | C2 | semidirect |
| 4. #19151931 | C2 | semidirect |
| 5. #19151893 | C2 | semidirect |
| 6. #19151890 | C2 | semidirect |
| 7. #19151837 | C2 | semidirect |
| 8. C4×#13083564 | C2 | semidirect |
| 10. C2×#15667945 | C2 | semidirect |
| 77. D4×C89 | Q16 | semidirect |
| 118. C89 | #3338 | semidirect |
| 198. D4 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152305 | 2 |
| #19152001 | 2 |
| #19151933 | 2 |
| #19151931 | 2 |
| #19151893 | 2 |
| #19151890 | 2 |
| #19151837 | 2 |
| C4×#13083564 | 2 |
| D4×#10623494 | 2 |
| C2×#15667945 | 2 |
| #554×C89 | 2 |
| #3338 | 89 |