Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
234 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 3. #24907060 | C2 | semidirect |
| 5. #24905520 | C2 | semidirect |
| 6. #24905513 | C2 | semidirect |
| 7. C83×#1367 | C2 | semidirect |
| 87. C8×C83 | SD32 | semidirect |
| 112. #1367 | D83 | semidirect |
| 115. C83 | #12420 | semidirect |
| 196. C8 | #14581737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909611 | 2 |
| #24909509 | 2 |
| #24907060 | 2 |
| C8×D664 | 2 |
| #24905520 | 2 |
| #24905513 | 2 |
| C83×#1367 | 2 |
| #12420 | 83 |