Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 1. Q8×D356 | C2 | semidirect |
| 2. #19152008 | C2 | semidirect |
| 3. #19151994 | C2 | semidirect |
| 4. #19151895 | C2 | semidirect |
| 5. #19151888 | C2 | semidirect |
| 6. #19151885 | C2 | semidirect |
| 7. #19151878 | C2 | semidirect |
| 8. #19151729 | C2 | semidirect |
| 11. #554×C89 | C2 | semidirect |
| 47. #13083559 | Q8 | semidirect |
| 78. D4×C89 | C2×Q8 | semidirect |
| 98. #10623494 | C2×Q8 | semidirect |
| 122. C89 | #3384 | semidirect |
| 123. #554 | D89 | semidirect |
| 204. D4 | 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 |
| #19151994 | 2 |
| #19151895 | 2 |
| #19151888 | 2 |
| #19151885 | 2 |
| #19151878 | 2 |
| #19151729 | 2 |
| #19151708 | 2 |
| C4×#13083559 | 2 |
| #554×C89 | 2 |
| #3384 | 89 |