Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
338 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 59 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. #19136776 | C2 | semidirect |
| 4. #19136035 | C2 | semidirect |
| 5. #19132611 | C2 | semidirect |
| 6. #19132611 | C2 | semidirect |
| 7. C43×#1315 | C2 | semidirect |
| 16. C2×#13063259 | C22 | semidirect |
| 23. #14582664 | C22 | semidirect |
| 25. C43×C22⋊C16 | C22 | semidirect |
| 26. C43×C22⋊C16 | C22 | semidirect |
| 163. #1315 | D43 | semidirect |
| 186. C22⋊C16 | C2×D43 | semidirect |
| 187. C22⋊C16 | 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 |
|---|---|
| #19145460 | 2 |
| #19136781 | 2 |
| #19136776 | 2 |
| #19136035 | 2 |
| #19132611 | 2 |
| C43×#1315 | 2 |
| #12284 | 43 |