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 |
|---|---|---|
| 1. #24909745 | C2 | semidirect |
| 4. #24905537 | C2 | semidirect |
| 5. #24905520 | C2 | semidirect |
| 6. #24905517 | C2 | semidirect |
| 65. C16×C83 | SD16 | semidirect |
| 110. C83 | #12453 | semidirect |
| 168. C16 | #13050578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909745 | 2 |
| #24906862 | 2 |
| #24906852 | 2 |
| #24905537 | 2 |
| #24905520 | 2 |
| #24905517 | 2 |
| D4×C16×C83 | 2 |
| #12453 | 83 |