Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
418 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 69 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. #19136818 | C2 | semidirect |
| 3. #19136743 | C2 | semidirect |
| 4. #19133995 | C2 | semidirect |
| 5. #19132555 | C2 | semidirect |
| 6. #19132549 | C2 | semidirect |
| 7. C43×#1361 | C2 | semidirect |
| 10. #14583304 | C22 | semidirect |
| 20. C4×C43⋊C16 | C22 | semidirect |
| 23. C43×C4⋊C16 | C22 | semidirect |
| 24. C43×#335 | C22 | semidirect |
| 148. #1361 | D43 | semidirect |
| 168. C4⋊C16 | C2×D43 | semidirect |
| 172. #335 | C2×D43 | semidirect |
| 174. C43 | #12372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19146270 | 2 |
| #19136818 | 2 |
| #19136743 | 2 |
| #19133995 | 2 |
| #19132555 | 2 |
| #19132549 | 2 |
| C43×#1361 | 2 |
| #12372 | 43 |