Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
294 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 65 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. #19147560 | C2 | semidirect |
| 5. #19132648 | C2 | semidirect |
| 6. #19132578 | C2 | semidirect |
| 7. C43×#1334 | C2 | semidirect |
| 68. Q16×C43 | SD16 | semidirect |
| 142. #1334 | D43 | semidirect |
| 166. C43 | #12361 | semidirect |
| 208. Q16 | #10621873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147560 | 2 |
| #19136837 | 2 |
| #19136635 | 2 |
| #19134080 | 2 |
| #19132648 | 2 |
| #19132578 | 2 |
| C43×#1334 | 2 |
| #12361 | 43 |