Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
560 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 91 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. #19143623 | C2 | semidirect |
| 3. C4×#13063241 | C2 | semidirect |
| 4. #19133193 | C2 | semidirect |
| 5. #19132461 | C2 | semidirect |
| 6. #19132460 | C2 | semidirect |
| 7. C43×#1527 | C2 | semidirect |
| 56. #13063236 | D4 | semidirect |
| 77. #97×C43 | D4 | semidirect |
| 235. #1527 | D43 | semidirect |
| 269. C43 | #9187 | semidirect |
| 309. #97 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19143623 | 2 |
| #19140448 | 2 |
| C4×#13063241 | 2 |
| #19133193 | 2 |
| #19132461 | 2 |
| #19132460 | 2 |
| C43×#1527 | 2 |
| #9187 | 43 |