Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
598 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 81 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. #24913323 | C2 | semidirect |
| 3. #24906086 | C2 | semidirect |
| 4. #24906010 | C2 | semidirect |
| 5. #24905910 | C2 | semidirect |
| 6. #24905329 | C2 | semidirect |
| 7. C83×#3112 | C2 | semidirect |
| 214. #3112 | D83 | semidirect |
| 220. C83 | #10020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917931 | 2 |
| #24913323 | 2 |
| #24906086 | 2 |
| #24906010 | 2 |
| #24905910 | 2 |
| #24905329 | 2 |
| C83×#3112 | 2 |
| #10020 | 83 |