Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1200 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1200 conjugacy classes of subgroups — too many to draw. Only its 155 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×#14583615 | C2 | semidirect |
| 2. C2×#14583072 | C2 | semidirect |
| 3. #19136620 | C2 | direct (N × H) |
| 4. C2×#14582698 | C2 | semidirect |
| 5. C2×#14582695 | C2 | semidirect |
| 6. C2×C43×#456 | C2 | semidirect |
| 10. #14583615 | C22 | semidirect |
| 17. #14583072 | C22 | semidirect |
| 20. #14582698 | C22 | semidirect |
| 21. #14582695 | C22 | semidirect |
| 26. C43×#456 | C22 | semidirect |
| 222. C2×#456 | D43 | semidirect |
| 230. C2×C43 | #2204 | semidirect |
| 246. #456 | C2×D43 | semidirect |
| 255. C43 | C2×#2204 | semidirect |
| 451. C2 | #19136620 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583615 | 2 |
| C2×#14583072 | 2 |
| #19136620 | 2 |
| C2×#14582698 | 2 |
| C2×#14582695 | 2 |
| C2×C43×#456 | 2 |
| C2×#2204 | 43 |