Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
960 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 123 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. #19135409 | C2 | semidirect |
| 3. C2×#14582639 | C2 | semidirect |
| 4. C2×#14582638 | C2 | semidirect |
| 5. C43×#1959 | C2 | semidirect |
| 8. #14583641 | C4 | semidirect |
| 16. C2×#13063236 | C22 | semidirect |
| 22. C2×#97×C43 | C22 | semidirect |
| 23. C43×#384 | C22 | semidirect |
| 194. #1959 | D43 | semidirect |
| 218. C2×#97 | C2×D43 | semidirect |
| 219. #384 | C2×D43 | semidirect |
| 222. C43 | #8506 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583641 | 2 |
| #19135409 | 2 |
| C2×#14582639 | 2 |
| C2×#14582638 | 2 |
| C43×#1959 | 2 |
| #8506 | 43 |