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. D4×Dic178 | C2 | semidirect |
| 2. #19152003 | C2 | semidirect |
| 3. #19152002 | C2 | semidirect |
| 4. #19151878 | C2 | semidirect |
| 5. #19151876 | C2 | semidirect |
| 6. C8×Dic178 | C2 | semidirect |
| 43. D8×C89 | Q8 | semidirect |
| 51. D4×C89 | C2×Q8 | semidirect |
| 63. Dic178 | D8 | direct (N × H) |
| 65. C8×C89 | C2×Q8 | semidirect |
| 84. C89 | Q8×D8 | semidirect |
| 119. D8 | Dic178 | direct (N × H) |
| 138. D4 | C2×Dic178 | semidirect |
| 150. C8 | C2×Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic178 | 2 |
| #19152003 | 2 |
| #19152002 | 2 |
| #19151878 | 2 |
| #19151876 | 2 |
| C8×Dic178 | 2 |
| D8×Dic89 | 2 |
| C4×D8×C89 | 2 |
| Q8×D8 | 89 |