Finite Group DatabasebetaFinite Group DatabasebetaOrder 11456.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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. #19153112 | C2 | semidirect |
| 2. #19153111 | C2 | semidirect |
| 3. #19153108 | C2 | semidirect |
| 4. #19153108 | C2 | semidirect |
| 5. #19153106 | C2 | semidirect |
| 6. #19153106 | C2 | semidirect |
| 7. #19153104 | C2 | semidirect |
| 8. #19153103 | C2 | semidirect |
| 12. #19153092 | C2 | semidirect |
| 13. #19153091 | C2 | semidirect |
| 14. #19153089 | C2 | semidirect |
| 15. C22⋊Q8×C179 | C2 | semidirect |
| 97. C179 | #563 | semidirect |
| 113. C22⋊Q8 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19153112 | 2 |
| #19153111 | 2 |
| #19153108 | 2 |
| #19153106 | 2 |
| #19153104 | 2 |
| #19153103 | 2 |
| #19153099 | 2 |
| #19153096 | 2 |
| #19153095 | 2 |
| #19153092 | 2 |
| #19153091 | 2 |
| #19153089 | 2 |
| C22⋊Q8×C179 | 2 |
| #563 | 179 |