Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
632 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 632 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. #19144604 | C2 | semidirect |
| 2. #19144394 | C2 | semidirect |
| 4. #19133158 | C2 | semidirect |
| 5. #19133019 | C2 | semidirect |
| 6. #19132987 | C2 | semidirect |
| 7. C43×#1286 | C2 | semidirect |
| 39. #13063325 | D4 | semidirect |
| 40. #13063325 | D4 | semidirect |
| 79. C4⋊C8×C43 | D4 | semidirect |
| 81. C4×C8×C43 | D4 | semidirect |
| 103. C2×D172 | SD16 | semidirect |
| 237. #1286 | D43 | semidirect |
| 270. C43 | #10000 | semidirect |
| 310. C4⋊C8 | D172 | semidirect |
| 318. C4×C8 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19144604 | 2 |
| #19144394 | 2 |
| #19139497 | 2 |
| #19133158 | 2 |
| #19133019 | 2 |
| #19132987 | 2 |
| C43×#1286 | 2 |
| #10000 | 43 |