Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14582732 | C2 | semidirect |
| 3. #366×D43 | C2 | semidirect |
| 4. #19132776 | C2 | semidirect |
| 5. #19132774 | C2 | semidirect |
| 6. #19132772 | C2 | semidirect |
| 7. C43×#1416 | C2 | semidirect |
| 10. #14583332 | C4 | semidirect |
| 31. D688 | C2×C4 | semidirect |
| 40. Q32×C43 | C2×C4 | semidirect |
| 104. #1416 | D43 | semidirect |
| 126. C43 | #13616 | semidirect |
| 136. Q32 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583332 | 2 |
| C2×#14582732 | 2 |
| #366×D43 | 2 |
| #19132776 | 2 |
| #19132774 | 2 |
| #19132772 | 2 |
| C43×#1416 | 2 |
| #13616 | 43 |