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×#19128081 | C2 | semidirect |
| 3. C2×#19127506 | C2 | semidirect |
| 5. C83×#1374 | C2 | semidirect |
| 96. C2×C4×C83 | SD32 | semidirect |
| 147. #1374 | D83 | semidirect |
| 148. C83 | #13327 | semidirect |
| 252. C2×C4 | #14581737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581737 | 2 |
| C2×#19128081 | 2 |
| C2×#19127506 | 2 |
| #24908329 | 2 |
| C83×#1374 | 2 |
| #13327 | 83 |