Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
562 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 103 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. #24918390 | C2 | semidirect |
| 2. C2×#19127991 | C2 | semidirect |
| 4. #24906147 | C2 | semidirect |
| 5. #24905863 | C2 | semidirect |
| 6. #24905359 | C2 | semidirect |
| 7. C83×#1460 | C2 | semidirect |
| 114. C2×D4×C83 | SD16 | semidirect |
| 215. #1460 | D83 | semidirect |
| 217. C83 | #10180 | semidirect |
| 305. C2×D4 | #13050579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918390 | 2 |
| C2×#19127991 | 2 |
| #24916927 | 2 |
| #24906147 | 2 |
| #24905863 | 2 |
| #24905359 | 2 |
| C83×#1460 | 2 |
| #10180 | 83 |