Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 1. #19136737 | C2 | semidirect |
| 4. #19132659 | C2 | semidirect |
| 5. #19132651 | C2 | semidirect |
| 7. C8×Q16×C43 | C2 | semidirect |
| 51. Q16×C43 | SD16 | semidirect |
| 91. C8×C43 | SD32 | semidirect |
| 110. C8×Q16 | D43 | semidirect |
| 133. C43 | #12417 | semidirect |
| 162. Q16 | #10621873 | semidirect |
| 202. C8 | #13063268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136737 | 2 |
| #19136635 | 2 |
| #19134187 | 2 |
| #19132659 | 2 |
| #19132651 | 2 |
| #19132640 | 2 |
| C8×Q16×C43 | 2 |
| #12417 | 43 |