Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
658 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#19128029 | C2 | semidirect |
| 3. C2×#19127438 | C2 | semidirect |
| 5. #24905730 | C2 | semidirect |
| 6. #24905306 | C2 | semidirect |
| 235. C83 | #9971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128029 | 2 |
| C2×#19128012 | 2 |
| C2×#19127438 | 2 |
| C2×#19127435 | 2 |
| #24905730 | 2 |
| #24905306 | 2 |
| C83×#2639 | 2 |
| #9971 | 83 |