Finite Group DatabasebetaFinite Group DatabasebetaOrder 11456.
152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 152 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 |
|---|---|---|
| 2. C2×#15668249 | C2 | semidirect |
| 3. C2×#15668246 | C2 | semidirect |
| 4. #19153036 | C2 | semidirect |
| 5. #19153033 | C2 | semidirect |
| 6. C22⋊(C179⋊C8) | C2 | semidirect |
| 7. C22⋊Q8×C179 | C2 | semidirect |
| 60. C179 | #452 | semidirect |
| 65. 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×#15668249 | 2 |
| C2×#15668246 | 2 |
| #19153036 | 2 |
| #19153033 | 2 |
| C22⋊(C179⋊C8) | 2 |
| C22⋊Q8×C179 | 2 |
| #452 | 179 |