Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
404 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 149 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. #19152001 | C2 | semidirect |
| 3. #19151878 | C2 | semidirect |
| 4. #19151875 | C2 | semidirect |
| 5. Q8×#10623494 | C2 | semidirect |
| 7. D4×Q8×C89 | C2 | semidirect |
| 28. #13083559 | Q8 | direct (N × H) |
| 47. Q8×C89 | D8 | semidirect |
| 49. D4×C89 | C2×Q8 | semidirect |
| 57. D356 | C2×Q8 | semidirect |
| 61. #10623494 | C2×Q8 | semidirect |
| 81. C89 | Q8×D8 | semidirect |
| 83. D4×Q8 | D89 | semidirect |
| 129. Q8 | #13083559 | direct (N × H) |
| 133. 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 |
| #19152001 | 2 |
| #19151878 | 2 |
| #19151875 | 2 |
| Q8×#10623494 | 2 |
| C4×#13083559 | 2 |
| D4×Q8×C89 | 2 |
| Q8×D8 | 89 |