Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
4614 conjugacy classes of subgroups; only the 491 normal subgroups are shown.
This group has 4614 conjugacy classes of subgroups — too many to draw. Only its 491 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 |
|---|---|---|
| 2. C2×#19127548 | C2 | semidirect |
| 3. #24905734 | C2 | semidirect |
| 4. #24905703 | C2 | semidirect |
| 5. C83×#1446 | C2 | semidirect |
| 7. C22×#13050591 | C4 | semidirect |
| 50. C22×Dic83 | #41 | semidirect |
| 53. C2×C4×D83 | C22⋊C4 | semidirect |
| 64. C22×C4×C83 | #41 | semidirect |
| 117. #1446 | D83 | semidirect |
| 119. C83 | #13851 | semidirect |
| 176. C22×C4 | #13050591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#13050591 | 2 |
| C2×#19127548 | 2 |
| #24905734 | 2 |
| #24905703 | 2 |
| C83×#1446 | 2 |
| #13851 | 83 |