Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
302 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 151 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. #19132517 | C2 | semidirect |
| 5. #19132516 | C2 | semidirect |
| 6. #19132515 | C2 | semidirect |
| 7. C43×#1313 | C2 | semidirect |
| 28. C16×D43 | C8 | semidirect |
| 53. C16×C43 | C2×C8 | semidirect |
| 55. C43⋊C16 | C2×C8 | semidirect |
| 85. #1313 | D43 | direct (N × H) |
| 88. D43 | #1313 | direct (N × H) |
| 102. C43 | C2×#1313 | semidirect |
| 137. C16 | C8×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #346×D43 | 2 |
| #322×D43 | 2 |
| #19132517 | 2 |
| #19132516 | 2 |
| #19132515 | 2 |
| C43×#1313 | 2 |
| C2×#1313 | 43 |