Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
218 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 85. C8×C83 | Q32 | semidirect |
| 109. C83 | #12421 | semidirect |
| 187. C8 | #14581738 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909615 | 2 |
| #24909513 | 2 |
| #24907060 | 2 |
| #24905527 | 2 |
| #24905522 | 2 |
| #24905511 | 2 |
| C8×Q16×C83 | 2 |
| #12421 | 83 |