Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
512 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 73 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×#14582695 | C2 | semidirect |
| 3. #19134996 | C2 | semidirect |
| 4. #19134809 | C2 | semidirect |
| 5. C43×#1394 | C2 | semidirect |
| 43. #13063244 | D4 | semidirect |
| 157. #1394 | D43 | semidirect |
| 178. C43 | #13426 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19141621 | 2 |
| C2×#14582695 | 2 |
| #19134996 | 2 |
| #19134809 | 2 |
| C43×#1394 | 2 |
| #13426 | 43 |