Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
266 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 73 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. #19151620 | C2 | semidirect |
| 3. C4×#13083557 | C2 | semidirect |
| 4. Q8⋊#10623494 | C2 | semidirect |
| 5. #19151327 | C2 | semidirect |
| 6. #19151325 | C2 | semidirect |
| 7. Q8⋊C8×C89 | C2 | semidirect |
| 61. Q8×C89 | M16 | semidirect |
| 73. D356 | M16 | semidirect |
| 111. C89 | #1489 | semidirect |
| 116. Q8⋊C8 | D89 | semidirect |
| 172. Q8 | #13083557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13083575 | 2 |
| #19151620 | 2 |
| C4×#13083557 | 2 |
| Q8⋊#10623494 | 2 |
| #19151327 | 2 |
| #19151325 | 2 |
| Q8⋊C8×C89 | 2 |
| #1489 | 89 |