Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
926 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 171 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. #24918661 | C2 | semidirect |
| 3. #24906774 | C2 | semidirect |
| 4. #24906761 | C2 | semidirect |
| 5. #24906098 | C2 | semidirect |
| 6. #24906078 | C2 | semidirect |
| 7. C83×#3550 | C2 | semidirect |
| 176. #3550 | D83 | semidirect |
| 183. C83 | #19054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918661 | 2 |
| #24917908 | 2 |
| #24906774 | 2 |
| #24906761 | 2 |
| #24906098 | 2 |
| #24906078 | 2 |
| C83×#3550 | 2 |
| #19054 | 83 |