Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
284 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 99 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. #19136877 | C2 | semidirect |
| 3. #19136823 | C2 | semidirect |
| 5. #19134192 | C2 | semidirect |
| 7. C8×C16×C43 | C2 | semidirect |
| 68. C16×C43 | SD16 | semidirect |
| 85. C8×C43 | SD32 | semidirect |
| 106. C8×C16 | D43 | semidirect |
| 126. C43 | #12505 | semidirect |
| 172. C16 | #10621873 | semidirect |
| 189. C8 | #13063270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136877 | 2 |
| #19136851 | 2 |
| #19136823 | 2 |
| #19136819 | 2 |
| #19134192 | 2 |
| #19134187 | 2 |
| C8×C16×C43 | 2 |
| #12505 | 43 |