Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
408 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 91 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×#19127528 | C2 | semidirect |
| 3. C2×#19127508 | C2 | semidirect |
| 4. C2×#19127486 | C2 | semidirect |
| 5. #24907528 | C2 | semidirect |
| 6. #24905572 | C2 | semidirect |
| 7. C83×#2139 | C2 | semidirect |
| 44. C2×C83⋊C16 | D4 | semidirect |
| 187. #2139 | D83 | semidirect |
| 191. C83 | #13385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917129 | 2 |
| C2×#19127528 | 2 |
| C2×#19127508 | 2 |
| C2×#19127486 | 2 |
| #24907528 | 2 |
| #24905572 | 2 |
| C83×#2139 | 2 |
| #13385 | 83 |