Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
564 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 113 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. #19143183 | C2 | semidirect |
| 3. #19136311 | C2 | semidirect |
| 4. C2×#14582680 | C2 | semidirect |
| 5. #19132701 | C2 | semidirect |
| 6. #19132700 | C2 | semidirect |
| 7. C43×#2140 | C2 | semidirect |
| 13. #14583149 | C4 | semidirect |
| 49. #13063259 | D4 | semidirect |
| 53. #13063257 | C2×C4 | semidirect |
| 62. C2×D8×C43 | C2×C4 | semidirect |
| 68. #107×C43 | D4 | semidirect |
| 184. #2140 | D43 | semidirect |
| 212. C43 | #12999 | semidirect |
| 221. C2×D8 | C4×D43 | semidirect |
| 250. #107 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583149 | 2 |
| #19143183 | 2 |
| #19136311 | 2 |
| C2×#14582680 | 2 |
| #19132701 | 2 |
| #19132700 | 2 |
| C43×#2140 | 2 |
| #12999 | 43 |