Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
364 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. #24907318 | C2 | semidirect |
| 3. #24906235 | C2 | semidirect |
| 6. #24905295 | C2 | semidirect |
| 7. C83×#1301 | C2 | semidirect |
| 17. #19127448 | C4 | semidirect |
| 18. #19127444 | C4 | semidirect |
| 161. #1301 | D83 | semidirect |
| 163. C83 | #9582 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24908290 | 2 |
| #24907318 | 2 |
| #24906235 | 2 |
| #24906113 | 2 |
| #24905863 | 2 |
| #24905295 | 2 |
| C83×#1301 | 2 |
| #9582 | 83 |