Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 109 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. #24920565 | C2 | semidirect |
| 3. #24909180 | C2 | semidirect |
| 4. #24909178 | C2 | semidirect |
| 5. #24907506 | C2 | semidirect |
| 6. #24905564 | C2 | semidirect |
| 7. C83×#1384 | C2 | semidirect |
| 15. #19127955 | C4 | semidirect |
| 49. C2×C83⋊C16 | D4 | semidirect |
| 60. C2×C16×C83 | D4 | semidirect |
| 176. #1384 | D83 | semidirect |
| 177. C83 | #13074 | semidirect |
| 226. C2×C16 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920565 | 2 |
| #24917112 | 2 |
| #24909180 | 2 |
| #24909178 | 2 |
| #24907506 | 2 |
| #24905564 | 2 |
| C83×#1384 | 2 |
| #13074 | 83 |