Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
786 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 187 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. C22×D688 | C2 | semidirect |
| 2. C22×#13063264 | C2 | semidirect |
| 3. C2×#14583136 | C2 | semidirect |
| 4. #19136699 | C2 | direct (N × H) |
| 5. C2×#14582699 | C2 | semidirect |
| 6. C2×C43×#367 | C2 | semidirect |
| 11. C2×D688 | C22 | semidirect |
| 13. C2×#13063264 | C22 | semidirect |
| 16. #14583136 | C22 | semidirect |
| 18. #14582699 | C22 | semidirect |
| 21. C43×#367 | C22 | semidirect |
| 44. C2×C16×C43 | D4 | semidirect |
| 78. C16×C43 | C2×D4 | semidirect |
| 127. C2×#367 | D43 | semidirect |
| 129. C2×C43 | #2218 | semidirect |
| 147. #367 | C2×D43 | semidirect |
| 149. C43 | C2×#2218 | semidirect |
| 171. C2×C16 | D172 | semidirect |
| 207. C16 | C2×D172 | semidirect |
| 252. C2 | #19136699 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D688 | 2 |
| C22×#13063264 | 2 |
| C2×#14583136 | 2 |
| #19136699 | 2 |
| C2×#14582699 | 2 |
| C2×C43×#367 | 2 |
| C2×#2218 | 43 |