Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
680 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 3. #19143463 | C2 | semidirect |
| 4. #19136659 | C2 | semidirect |
| 5. #19136643 | C2 | semidirect |
| 6. #19136353 | C2 | semidirect |
| 7. #19136315 | C2 | semidirect |
| 9. C22×Q32×C43 | C2 | semidirect |
| 169. C22×Q32 | D43 | semidirect |
| 206. C43 | #33588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583340 | 2 |
| #19145084 | 2 |
| #19143463 | 2 |
| #19136659 | 2 |
| #19136643 | 2 |
| #19136353 | 2 |
| #19136315 | 2 |
| #19136303 | 2 |
| C22×Q32×C43 | 2 |
| #33588 | 43 |