Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 566 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. C2×#14582719 | C2 | semidirect |
| 3. C2×#14582713 | C2 | semidirect |
| 4. C2×#14582712 | C2 | semidirect |
| 5. #19136310 | C2 | semidirect |
| 6. #19134476 | C2 | semidirect |
| 7. C43×#2140 | C2 | semidirect |
| 13. #14583274 | C4 | semidirect |
| 47. #13063261 | D4 | semidirect |
| 64. #107×C43 | D4 | semidirect |
| 172. #2140 | D43 | semidirect |
| 198. C43 | #13261 | semidirect |
| 233. #107 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583274 | 2 |
| C2×#14582719 | 2 |
| C2×#14582713 | 2 |
| C2×#14582712 | 2 |
| #19136310 | 2 |
| #19134476 | 2 |
| C43×#2140 | 2 |
| #13261 | 43 |