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. #19152321 | C2 | semidirect |
| 2. Q8×D356 | C2 | semidirect |
| 3. #19151958 | C2 | semidirect |
| 4. #19151949 | C2 | semidirect |
| 5. #19151894 | C2 | semidirect |
| 6. #19151879 | C2 | semidirect |
| 8. #19151804 | C2 | semidirect |
| 9. #19151700 | C2 | semidirect |
| 11. #446×C89 | C2 | semidirect |
| 123. C89 | #3367 | semidirect |
| 132. #446 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152321 | 2 |
| Q8×D356 | 2 |
| #19151958 | 2 |
| #19151949 | 2 |
| #19151894 | 2 |
| #19151879 | 2 |
| #19151814 | 2 |
| #19151804 | 2 |
| #19151700 | 2 |
| C4×D712 | 2 |
| #446×C89 | 2 |
| #3367 | 89 |