Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
166 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 3. #19151348 | C2 | semidirect |
| 4. Q8⋊#10623494 | C2 | semidirect |
| 6. #19151319 | C2 | semidirect |
| 7. C8×Q8×C89 | C2 | semidirect |
| 43. Q8×C89 | M16 | semidirect |
| 56. C8×C89 | SD16 | semidirect |
| 78. C89 | #1583 | semidirect |
| 79. C8×Q8 | D89 | semidirect |
| 121. Q8 | #13083557 | semidirect |
| 138. C8 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13083561 | 2 |
| #19151677 | 2 |
| #19151348 | 2 |
| Q8⋊#10623494 | 2 |
| #19151325 | 2 |
| #19151319 | 2 |
| C8×Q8×C89 | 2 |
| #1583 | 89 |