Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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. #24909720 | C2 | semidirect |
| 2. #24909713 | C2 | semidirect |
| 3. #24909712 | C2 | semidirect |
| 4. #24907077 | C2 | semidirect |
| 5. #24907070 | C2 | semidirect |
| 6. #24905379 | C2 | semidirect |
| 7. C83×#2248 | C2 | semidirect |
| 53. C83⋊C16 | D8 | semidirect |
| 65. C16×C83 | D8 | semidirect |
| 104. #2248 | D83 | semidirect |
| 110. C83 | #12519 | semidirect |
| 168. C16 | #13050575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909720 | 2 |
| #24909713 | 2 |
| #24909712 | 2 |
| #24907077 | 2 |
| #24907070 | 2 |
| #24905379 | 2 |
| C83×#2248 | 2 |
| #12519 | 83 |