Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
610 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 125 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. #19135435 | C2 | semidirect |
| 3. #19133353 | C2 | semidirect |
| 4. #19133264 | C2 | semidirect |
| 5. #19133263 | C2 | semidirect |
| 6. M16×C43⋊C8 | C2 | semidirect |
| 7. C43×#1965 | C2 | semidirect |
| 89. M16×C43 | D8 | semidirect |
| 142. C43⋊C8 | #100 | semidirect |
| 165. #1965 | D43 | semidirect |
| 194. C43 | #9802 | semidirect |
| 261. M16 | #10621882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583275 | 2 |
| #19135435 | 2 |
| #19133353 | 2 |
| #19133264 | 2 |
| #19133263 | 2 |
| M16×C43⋊C8 | 2 |
| C43×#1965 | 2 |
| #9802 | 43 |