Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
298 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 71 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. #24909690 | C2 | semidirect |
| 3. #24909510 | C2 | semidirect |
| 4. #24905522 | C2 | semidirect |
| 5. #24905426 | C2 | semidirect |
| 89. D4×C83 | Q32 | semidirect |
| 135. C83 | #12346 | semidirect |
| 220. D4 | #14581738 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24919856 | 2 |
| #24909690 | 2 |
| #24909510 | 2 |
| #24905522 | 2 |
| #24905426 | 2 |
| D4⋊(C83⋊C16) | 2 |
| C83×#1669 | 2 |
| #12346 | 83 |