Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
2130 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2130 conjugacy classes of subgroups — too many to draw. Only its 667 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. #24915845 | C2 | semidirect |
| 2. #24915830 | C2 | semidirect |
| 3. #24915778 | C2 | semidirect |
| 4. C4×#14581786 | C2 | semidirect |
| 6. #24909946 | C2 | semidirect |
| 7. C2×C43×C83 | C2 | semidirect |
| 70. C42×C83 | #41 | semidirect |
| 79. C2×C4×C83 | #126 | semidirect |
| 112. C2×C43 | D83 | semidirect |
| 113. C83 | #36641 | semidirect |
| 176. C42 | #13050590 | semidirect |
| 192. C2×C4 | #14581786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24915845 | 2 |
| #24915830 | 2 |
| #24915778 | 2 |
| C4×#14581786 | 2 |
| #24909953 | 2 |
| #24909946 | 2 |
| C2×C43×C83 | 2 |
| #36641 | 83 |