Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
472 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 70. Q8×C43 | Q32 | semidirect |
| 122. C43 | #33930 | semidirect |
| 174. Q8 | Dic344 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147601 | 2 |
| Q8×Dic172 | 2 |
| #19136823 | 2 |
| #19136748 | 2 |
| #19136646 | 2 |
| C4×Dic344 | 2 |
| Q8×C16×C43 | 2 |
| #33930 | 43 |