Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
324 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #24905434 | C2 | semidirect |
| 5. #24905433 | C2 | semidirect |
| 6. #24905432 | C2 | semidirect |
| 7. C83×#1334 | C2 | semidirect |
| 154. #1334 | D83 | semidirect |
| 155. C83 | #11681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918046 | 2 |
| #24909056 | 2 |
| #24906217 | 2 |
| #24905434 | 2 |
| #24905433 | 2 |
| #24905432 | 2 |
| C83×#1334 | 2 |
| #11681 | 83 |