Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 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. #19152008 | C2 | semidirect |
| 3. #19152001 | C2 | semidirect |
| 5. #19151893 | C2 | semidirect |
| 6. #19151883 | C2 | semidirect |
| 8. #19151729 | C2 | semidirect |
| 11. #557×C89 | C2 | semidirect |
| 47. #13083561 | Q8 | semidirect |
| 77. Q8×C89 | C2×Q8 | semidirect |
| 96. #10623494 | C2×Q8 | semidirect |
| 117. C89 | #3386 | semidirect |
| 118. #557 | D89 | semidirect |
| 196. Q8 | Q8×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D356 | 2 |
| #19152008 | 2 |
| #19152001 | 2 |
| #19151895 | 2 |
| #19151893 | 2 |
| #19151883 | 2 |
| #19151875 | 2 |
| #19151729 | 2 |
| #19151696 | 2 |
| C4×#13083561 | 2 |
| #557×C89 | 2 |
| #3386 | 89 |