Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#19128136 | C2 | semidirect |
| 2. C2×#19127971 | C2 | semidirect |
| 3. C2×#19127508 | C2 | semidirect |
| 4. C2×#19127501 | C2 | semidirect |
| 5. C2×#19127485 | C2 | semidirect |
| 6. #24905571 | C2 | semidirect |
| 7. C83×#3061 | C2 | semidirect |
| 40. C2×D664 | D4 | semidirect |
| 46. #14581732 | D4 | semidirect |
| 52. #14581728 | D4 | semidirect |
| 221. #3061 | D83 | semidirect |
| 226. C83 | #13307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128136 | 2 |
| C2×#19127971 | 2 |
| C2×#19127508 | 2 |
| C2×#19127501 | 2 |
| C2×#19127485 | 2 |
| #24905571 | 2 |
| C83×#3061 | 2 |
| #13307 | 83 |