Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
340 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 1. #24909713 | C2 | semidirect |
| 2. #24909712 | C2 | semidirect |
| 3. #24909688 | C2 | semidirect |
| 4. #24907077 | C2 | semidirect |
| 5. #24907056 | C2 | semidirect |
| 6. #24905382 | C2 | semidirect |
| 7. C83×#2240 | C2 | semidirect |
| 97. C83⋊C8 | D16 | semidirect |
| 123. #2240 | D83 | semidirect |
| 127. C83 | #12525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909713 | 2 |
| #24909712 | 2 |
| #24909688 | 2 |
| #24907077 | 2 |
| #24907056 | 2 |
| #24905382 | 2 |
| C83×#2240 | 2 |
| #12525 | 83 |