Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
650 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 103 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×#14583334 | C2 | semidirect |
| 2. C2×#14583276 | C2 | semidirect |
| 3. C2×#14582711 | C2 | semidirect |
| 4. #19132677 | C2 | semidirect |
| 5. C43×#1974 | C2 | semidirect |
| 37. #13063265 | D4 | semidirect |
| 42. C2×Q16×C43 | D4 | semidirect |
| 44. C2×D8×C43 | D4 | semidirect |
| 145. #1974 | D43 | semidirect |
| 168. C43 | #13331 | semidirect |
| 174. C2×Q16 | D172 | semidirect |
| 185. C2×D8 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583334 | 2 |
| C2×#14583276 | 2 |
| C2×#14582711 | 2 |
| #19132677 | 2 |
| C43×#1974 | 2 |
| #13331 | 43 |