Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
460 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 460 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 |
|---|---|---|
| 1. #19152270 | C2 | semidirect |
| 2. #19151974 | C2 | semidirect |
| 3. #19151793 | C2 | semidirect |
| 4. #19151790 | C2 | semidirect |
| 5. Q8×#10623494 | C2 | semidirect |
| 6. C4×#13083559 | C2 | semidirect |
| 7. #550×C89 | C2 | semidirect |
| 47. Q8×C89 | D8 | semidirect |
| 64. #10623494 | #41 | semidirect |
| 84. C89 | #3391 | semidirect |
| 86. #550 | D89 | semidirect |
| 131. Q8 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152270 | 2 |
| #19151974 | 2 |
| #19151793 | 2 |
| #19151790 | 2 |
| Q8×#10623494 | 2 |
| C4×#13083559 | 2 |
| #550×C89 | 2 |
| #3391 | 89 |