Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
464 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 79 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. #24907896 | C2 | semidirect |
| 5. #24905826 | C2 | semidirect |
| 6. #24905368 | C2 | semidirect |
| 7. C83×#1855 | C2 | semidirect |
| 218. #1855 | D83 | semidirect |
| 222. C83 | #10562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918270 | 2 |
| #24907926 | 2 |
| #24907896 | 2 |
| #24906032 | 2 |
| #24905826 | 2 |
| #24905368 | 2 |
| C83×#1855 | 2 |
| #10562 | 83 |