Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
866 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 866 conjugacy classes of subgroups — too many to draw. Only its 267 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. C2×#14583297 | C2 | semidirect |
| 3. C2×#14583250 | C2 | semidirect |
| 5. #19134196 | C2 | direct (N × H) |
| 6. C2×C82×C43 | C2 | semidirect |
| 12. #14583297 | C22 | semidirect |
| 16. #14583250 | C22 | semidirect |
| 24. C82×C43 | C22 | semidirect |
| 127. C2×C82 | D43 | semidirect |
| 128. C2×C43 | #1708 | semidirect |
| 149. C82 | C2×D43 | semidirect |
| 150. C43 | C2×#1708 | semidirect |
| 248. C2 | #19134196 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583297 | 2 |
| C2×#14583272 | 2 |
| C2×#14583250 | 2 |
| C2×#14583246 | 2 |
| #19134196 | 2 |
| C2×C82×C43 | 2 |
| C2×#1708 | 43 |