Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
504 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #19135920 | C2 | semidirect |
| 3. #19135695 | C2 | semidirect |
| 4. #19132420 | C2 | semidirect |
| 5. #19132417 | C2 | semidirect |
| 73. C2×D4×C43 | Q16 | semidirect |
| 233. C43 | #7756 | semidirect |
| 284. C2×D4 | #10621885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19141612 | 2 |
| #19135920 | 2 |
| #19135695 | 2 |
| #19132420 | 2 |
| #19132417 | 2 |
| #19132416 | 2 |
| C43×#2023 | 2 |
| #7756 | 43 |