Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
594 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 129 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×#19127505 | C2 | semidirect |
| 4. #24905541 | C2 | semidirect |
| 5. C2×#494×C83 | C2 | semidirect |
| 103. C2×C4×C83 | SD32 | semidirect |
| 144. C2×#494 | D83 | semidirect |
| 148. C83 | #13327 | semidirect |
| 252. C2×C4 | #14581735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581735 | 2 |
| C2×#19127505 | 2 |
| #24908329 | 2 |
| #24905541 | 2 |
| C2×#494×C83 | 2 |
| #13327 | 83 |