Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
404 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 141 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. #19152327 | C2 | semidirect |
| 3. #19151971 | C2 | semidirect |
| 4. #19151804 | C2 | semidirect |
| 5. #19151799 | C2 | semidirect |
| 6. C4×#13083563 | C2 | semidirect |
| 7. C8×Q8×C89 | C2 | semidirect |
| 45. Q8×C89 | SD16 | semidirect |
| 60. C8×C89 | #41 | semidirect |
| 77. C89 | #3392 | semidirect |
| 83. C8×Q8 | D89 | semidirect |
| 124. Q8 | #13083563 | semidirect |
| 137. C8 | #13083575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152327 | 2 |
| #19152270 | 2 |
| #19151971 | 2 |
| #19151804 | 2 |
| #19151799 | 2 |
| C4×#13083563 | 2 |
| C8×Q8×C89 | 2 |
| #3392 | 89 |