Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 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. C2×#19127512 | C2 | semidirect |
| 4. #24909190 | C2 | semidirect |
| 5. #24907519 | C2 | semidirect |
| 6. #24905563 | C2 | semidirect |
| 7. C83×#1388 | C2 | semidirect |
| 15. #19127977 | C4 | semidirect |
| 16. #19127972 | C4 | semidirect |
| 184. #1388 | D83 | semidirect |
| 186. C83 | #13070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920565 | 2 |
| #24917184 | 2 |
| C2×#19127512 | 2 |
| #24909190 | 2 |
| #24907519 | 2 |
| #24905563 | 2 |
| C83×#1388 | 2 |
| #13070 | 83 |