Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
492 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 3. C2×#14582703 | C2 | semidirect |
| 5. #19132704 | C2 | semidirect |
| 6. #19132690 | C2 | semidirect |
| 7. C43×#2141 | C2 | semidirect |
| 13. #14583171 | C4 | semidirect |
| 51. #13063261 | C2×C4 | semidirect |
| 63. C2×Q16×C43 | C2×C4 | semidirect |
| 178. #2141 | D43 | semidirect |
| 209. C43 | #12997 | semidirect |
| 220. C2×Q16 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583171 | 2 |
| #19143192 | 2 |
| C2×#14582703 | 2 |
| C2×#14582684 | 2 |
| #19132704 | 2 |
| #19132690 | 2 |
| C43×#2141 | 2 |
| #12997 | 43 |