Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
312 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 107 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. #24909228 | C2 | semidirect |
| 4. #24909060 | C2 | semidirect |
| 6. #24905553 | C2 | semidirect |
| 7. C83×#1378 | C2 | semidirect |
| 148. #1378 | D83 | semidirect |
| 149. C83 | #13123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909228 | 2 |
| #24909090 | 2 |
| C2×#19127486 | 2 |
| #24909060 | 2 |
| #24907264 | 2 |
| #24905553 | 2 |
| C83×#1378 | 2 |
| #13123 | 83 |