Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
958 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 958 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. C2×#14583269 | C2 | semidirect |
| 2. C2×#14583258 | C2 | semidirect |
| 3. #19133918 | C2 | direct (N × H) |
| 4. C2×#14582641 | C2 | semidirect |
| 5. C2×#14582639 | C2 | semidirect |
| 9. #14583269 | C22 | semidirect |
| 11. #14583258 | C22 | semidirect |
| 17. #14582641 | C22 | semidirect |
| 18. #14582639 | C22 | semidirect |
| 152. C2×C43 | #1662 | semidirect |
| 175. C43 | C2×#1662 | semidirect |
| 294. C2 | #19133918 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583269 | 2 |
| C2×#14583258 | 2 |
| #19133918 | 2 |
| C2×#14582641 | 2 |
| C2×#14582639 | 2 |
| C2×C43×#562 | 2 |
| C2×#1662 | 43 |