Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. D4×Dic178 | C2 | semidirect |
| 2. #19152263 | C2 | semidirect |
| 3. #19152002 | C2 | semidirect |
| 4. #19152001 | C2 | semidirect |
| 5. #19151879 | C2 | semidirect |
| 6. #19151877 | C2 | semidirect |
| 7. #19151876 | C2 | semidirect |
| 8. #19151722 | C2 | semidirect |
| 11. #474×C89 | C2 | semidirect |
| 51. #13083559 | Q8 | semidirect |
| 78. D4×C89 | C2×Q8 | semidirect |
| 91. D356 | C2×Q8 | semidirect |
| 97. Dic178 | D8 | semidirect |
| 100. #10623494 | C2×Q8 | semidirect |
| 124. C89 | Q8×D8 | semidirect |
| 132. #474 | D89 | semidirect |
| 208. D4 | Q8×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic178 | 2 |
| #19152263 | 2 |
| #19152002 | 2 |
| #19152001 | 2 |
| #19151879 | 2 |
| #19151877 | 2 |
| #19151876 | 2 |
| #19151722 | 2 |
| C4×#13083559 | 2 |
| #19151678 | 2 |
| #474×C89 | 2 |
| Q8×D8 | 89 |