Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
248 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #19151330 | C2 | semidirect |
| 5. Q8⋊#10623494 | C2 | semidirect |
| 6. #19151328 | C2 | semidirect |
| 7. Q8⋊C8×C89 | C2 | semidirect |
| 59. Q8×C89 | M16 | semidirect |
| 79. Dic178 | M16 | semidirect |
| 105. C89 | #1487 | semidirect |
| 112. Q8⋊C8 | D89 | semidirect |
| 167. Q8 | #13083557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D89 | 2 |
| #19151649 | 2 |
| #19151620 | 2 |
| #19151330 | 2 |
| Q8⋊#10623494 | 2 |
| #19151328 | 2 |
| Q8⋊C8×C89 | 2 |
| #1487 | 89 |