Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
422 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 57 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. #19136512 | C2 | semidirect |
| 3. #19135714 | C2 | semidirect |
| 4. #19132611 | C2 | semidirect |
| 5. #19132610 | C2 | semidirect |
| 6. #19132520 | C2 | semidirect |
| 7. C43×#2185 | C2 | semidirect |
| 20. C22⋊(C43⋊C16) | C22 | semidirect |
| 21. #14582664 | C22 | semidirect |
| 22. C22×Q16×C43 | C22 | semidirect |
| 26. C43×C22⋊C16 | C22 | semidirect |
| 180. #2185 | D43 | semidirect |
| 193. C22×Q16 | C2×D43 | semidirect |
| 209. C22⋊C16 | C2×D43 | semidirect |
| 211. C43 | #12111 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145455 | 2 |
| #19136512 | 2 |
| #19135714 | 2 |
| #19132611 | 2 |
| #19132610 | 2 |
| #19132520 | 2 |
| C43×#2185 | 2 |
| #12111 | 43 |