Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
382 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 382 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. #24909265 | C2 | semidirect |
| 3. #24909264 | C2 | semidirect |
| 4. #24905422 | C2 | semidirect |
| 5. #24905421 | C2 | semidirect |
| 6. #24905420 | C2 | semidirect |
| 7. C83×#1330 | C2 | semidirect |
| 18. C4⋊(C83⋊C16) | C22 | semidirect |
| 22. #19127477 | C22 | semidirect |
| 25. C4⋊C16×C83 | C22 | semidirect |
| 26. #346×C83 | C22 | semidirect |
| 176. #1330 | D83 | semidirect |
| 177. C83 | #11636 | semidirect |
| 191. C4⋊C16 | C2×D83 | semidirect |
| 196. #346 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #436×D83 | 2 |
| #24909265 | 2 |
| #24909264 | 2 |
| #24905422 | 2 |
| #24905421 | 2 |
| #24905420 | 2 |
| C83×#1330 | 2 |
| #11636 | 83 |