Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
338 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 338 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. #19136781 | C2 | semidirect |
| 3. #19136773 | C2 | semidirect |
| 4. #19136037 | C2 | semidirect |
| 5. #19132609 | C2 | semidirect |
| 6. #19132520 | C2 | semidirect |
| 7. C43×#1349 | C2 | semidirect |
| 15. C2×#13063259 | C22 | semidirect |
| 22. C22⋊(C43⋊C16) | C22 | semidirect |
| 25. C43×C22⋊C16 | C22 | semidirect |
| 26. C43×#341 | C22 | semidirect |
| 162. #1349 | D43 | semidirect |
| 187. C22⋊C16 | C2×D43 | semidirect |
| 189. #341 | C2×D43 | semidirect |
| 190. C43 | #12284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145455 | 2 |
| #19136781 | 2 |
| #19136773 | 2 |
| #19136037 | 2 |
| #19132609 | 2 |
| #19132520 | 2 |
| C43×#1349 | 2 |
| #12284 | 43 |