Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. Q8×D356 | C2 | semidirect |
| 2. #19151957 | C2 | semidirect |
| 3. #19151948 | C2 | semidirect |
| 4. #19151893 | C2 | semidirect |
| 5. #19151878 | C2 | semidirect |
| 7. #19151800 | C2 | semidirect |
| 8. #19151729 | C2 | semidirect |
| 9. #19151696 | C2 | semidirect |
| 11. #556×C89 | C2 | semidirect |
| 123. C89 | #3367 | semidirect |
| 124. #556 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D356 | 2 |
| #19151957 | 2 |
| #19151948 | 2 |
| #19151893 | 2 |
| #19151878 | 2 |
| #19151810 | 2 |
| #19151800 | 2 |
| #19151729 | 2 |
| #19151696 | 2 |
| C4×#13083559 | 2 |
| #556×C89 | 2 |
| #3367 | 89 |