Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 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. C22×Dic356 | C2 | semidirect |
| 3. #19151978 | C2 | semidirect |
| 4. #19151839 | C2 | semidirect |
| 5. #19151809 | C2 | semidirect |
| 6. #19151756 | C2 | semidirect |
| 7. C4×Dic356 | C2 | semidirect |
| 38. Dic356 | D4 | direct (N × H) |
| 56. D4×C89 | Q16 | semidirect |
| 77. C22×C89 | C2×Q16 | semidirect |
| 81. C4×C89 | C2×Q16 | semidirect |
| 92. C89 | D4×Q16 | semidirect |
| 153. D4 | Dic356 | direct (N × H) |
| 169. C22 | C2×Dic356 | semidirect |
| 176. C4 | C2×Dic356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic356 | 2 |
| D4×Dic178 | 2 |
| #19151978 | 2 |
| #19151839 | 2 |
| #19151809 | 2 |
| #19151756 | 2 |
| C4×Dic356 | 2 |
| C8×D4×C89 | 2 |
| D4×Q16 | 89 |