Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
624 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 127 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. #24916027 | C2 | semidirect |
| 3. #24906130 | C2 | semidirect |
| 4. #24905322 | C2 | semidirect |
| 5. C83×#1458 | C2 | semidirect |
| 42. C4⋊(C83⋊C8) | D4 | semidirect |
| 188. #1458 | D83 | semidirect |
| 190. C83 | #9197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916027 | 2 |
| #24913213 | 2 |
| #24906130 | 2 |
| #24905322 | 2 |
| C83×#1458 | 2 |
| #9197 | 83 |