Finite Group DatabasebetaFinite Group DatabasebetaOrder 11456.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. C2×Q8×D179 | C2 | semidirect |
| 3. #19153112 | C2 | semidirect |
| 4. #19153099 | C2 | semidirect |
| 5. #19153098 | C2 | semidirect |
| 6. #19153095 | C2 | semidirect |
| 7. #19153093 | C2 | semidirect |
| 8. #19153092 | C2 | semidirect |
| 9. #19153089 | C2 | semidirect |
| 10. #19153071 | C2 | semidirect |
| 11. C22⋊Q8×C179 | C2 | semidirect |
| 83. C179 | #536 | semidirect |
| 94. C22⋊Q8 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668259 | 2 |
| C2×Q8×D179 | 2 |
| #19153112 | 2 |
| #19153099 | 2 |
| #19153098 | 2 |
| #19153095 | 2 |
| #19153093 | 2 |
| #19153092 | 2 |
| #19153089 | 2 |
| #19153071 | 2 |
| C22⋊Q8×C179 | 2 |
| #536 | 179 |