Finite Group DatabasebetaFinite Group DatabasebetaOrder 11456.
144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 43 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. C2×#15668248 | C2 | semidirect |
| 2. C2×#15668247 | C2 | semidirect |
| 3. C2×#15668244 | C2 | semidirect |
| 4. #19153109 | C2 | semidirect |
| 5. #19153100 | C2 | semidirect |
| 6. #19153023 | C2 | semidirect |
| 7. C2×D8×C179 | C2 | semidirect |
| 29. C179⋊C8 | D4 | semidirect |
| 37. C8×C179 | D4 | semidirect |
| 54. C179 | #496 | semidirect |
| 59. C2×D8 | D179 | semidirect |
| 92. C8 | C22⋊D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668248 | 2 |
| C2×#15668247 | 2 |
| C2×#15668244 | 2 |
| #19153109 | 2 |
| #19153100 | 2 |
| #19153023 | 2 |
| C2×D8×C179 | 2 |
| #496 | 179 |