Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
226 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 25. #14581738 | C8 | direct (N × H) |
| 82. C8×C83 | Q32 | semidirect |
| 107. C83 | C8×Q32 | semidirect |
| 183. C8 | #14581738 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14581738 | 2 |
| C8×Dic332 | 2 |
| #24905534 | 2 |
| #24905427 | 2 |
| #24905426 | 2 |
| C8×C83⋊C16 | 2 |
| C8×Q16×C83 | 2 |
| C8×Q32 | 83 |