Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
424 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 133 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. #19151911 | C2 | semidirect |
| 3. #19151893 | C2 | semidirect |
| 4. #19151798 | C2 | semidirect |
| 5. #19151737 | C2 | semidirect |
| 6. #19151696 | C2 | semidirect |
| 7. #19151655 | C2 | semidirect |
| 8. C2×C4×Q8×C89 | C2 | semidirect |
| 68. Q8×C89 | #41 | semidirect |
| 112. C89 | #3112 | semidirect |
| 114. C2×C4×Q8 | D89 | semidirect |
| 181. Q8 | #13083574 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152148 | 2 |
| #19151911 | 2 |
| #19151893 | 2 |
| #19151798 | 2 |
| #19151737 | 2 |
| #19151696 | 2 |
| #19151655 | 2 |
| C2×C4×Q8×C89 | 2 |
| #3112 | 89 |