Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1218 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1218 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 1. C22×#14581784 | C2 | semidirect |
| 2. C2×#19128066 | C2 | semidirect |
| 4. #24908610 | C2 | semidirect |
| 5. #24908432 | C2 | semidirect |
| 6. #24907778 | C2 | semidirect |
| 7. C83×#1749 | C2 | semidirect |
| 35. #14581784 | D4 | semidirect |
| 137. C22×C83 | #490 | semidirect |
| 168. #1749 | D83 | semidirect |
| 169. C83 | #25913 | semidirect |
| 304. C22 | #19128066 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581784 | 2 |
| C2×#19128066 | 2 |
| #24915808 | 2 |
| #24908610 | 2 |
| #24908432 | 2 |
| #24907778 | 2 |
| C83×#1749 | 2 |
| #25913 | 83 |