Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
574 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 4. #19133042 | C2 | semidirect |
| 5. #19132488 | C2 | semidirect |
| 6. #19132451 | C2 | semidirect |
| 7. C43×#2276 | C2 | semidirect |
| 10. #14583194 | C4 | semidirect |
| 11. #14583099 | C4 | semidirect |
| 121. Q8×C43 | #104 | semidirect |
| 179. #2276 | D43 | semidirect |
| 212. C43 | #9326 | semidirect |
| 306. Q8 | #13063253 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19144717 | 2 |
| #19135513 | 2 |
| #19133102 | 2 |
| #19133042 | 2 |
| #19132488 | 2 |
| #19132451 | 2 |
| C43×#2276 | 2 |
| #9326 | 43 |