Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
684 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 85 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. #24918468 | C2 | semidirect |
| 2. #24917838 | C2 | semidirect |
| 4. #24906176 | C2 | semidirect |
| 5. #24906060 | C2 | semidirect |
| 6. #24905974 | C2 | semidirect |
| 7. C83×#1300 | C2 | semidirect |
| 39. #14581792 | D4 | semidirect |
| 40. #14581792 | D4 | semidirect |
| 70. C4⋊C8×C83 | D4 | semidirect |
| 73. #97×C83 | D4 | semidirect |
| 207. #1300 | D83 | semidirect |
| 208. C83 | #10096 | semidirect |
| 265. C4⋊C8 | D332 | semidirect |
| 274. #97 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918468 | 2 |
| #24917838 | 2 |
| #24913569 | 2 |
| #24906176 | 2 |
| #24906060 | 2 |
| #24905974 | 2 |
| C83×#1300 | 2 |
| #10096 | 83 |