Finite Group DatabasebetaFinite Group DatabasebetaOrder 11456.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #19153106 | C2 | semidirect |
| 2. #19153104 | C2 | semidirect |
| 3. #19153100 | C2 | semidirect |
| 4. #19153095 | C2 | semidirect |
| 5. #19153093 | C2 | semidirect |
| 7. C4×Dic358 | C2 | semidirect |
| 8. C4×C22⋊D179 | C2 | semidirect |
| 9. #19153072 | C2 | semidirect |
| 10. C42×D179 | C2 | semidirect |
| 11. C4×D4×C179 | C2 | semidirect |
| 74. C179 | #529 | semidirect |
| 84. C4×D4 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19153106 | 2 |
| #19153104 | 2 |
| #19153100 | 2 |
| #19153095 | 2 |
| #19153093 | 2 |
| #19153084 | 2 |
| C4×Dic358 | 2 |
| C4×C22⋊D179 | 2 |
| #19153072 | 2 |
| C42×D179 | 2 |
| C4×D4×C179 | 2 |
| #529 | 179 |