Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 141 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. #19151948 | C2 | semidirect |
| 3. #19151926 | C2 | semidirect |
| 4. #19151883 | C2 | semidirect |
| 5. #19151829 | C2 | semidirect |
| 6. #19151800 | C2 | semidirect |
| 7. #19151737 | C2 | semidirect |
| 8. C4×#13083561 | C2 | semidirect |
| 9. D4×#10623494 | C2 | semidirect |
| 10. C2×#15667936 | C2 | semidirect |
| 11. D4×Q8×C89 | C2 | semidirect |
| 83. Q8×C89 | #41 | semidirect |
| 84. D4×C89 | SD16 | semidirect |
| 129. C89 | #3298 | semidirect |
| 130. D4×Q8 | D89 | semidirect |
| 213. Q8 | #13083573 | semidirect |
| 217. D4 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152252 | 2 |
| #19151948 | 2 |
| #19151926 | 2 |
| #19151883 | 2 |
| #19151829 | 2 |
| #19151800 | 2 |
| #19151737 | 2 |
| C4×#13083561 | 2 |
| D4×#10623494 | 2 |
| C2×#15667936 | 2 |
| D4×Q8×C89 | 2 |
| #3298 | 89 |