Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
678 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 107 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. #24918770 | C2 | semidirect |
| 2. #24918378 | C2 | semidirect |
| 3. #24917915 | C2 | semidirect |
| 4. #24908390 | C2 | semidirect |
| 5. #24905957 | C2 | semidirect |
| 6. #24905314 | C2 | semidirect |
| 7. C83×#1980 | C2 | semidirect |
| 123. M16×C83 | D8 | semidirect |
| 225. #1980 | D83 | semidirect |
| 228. C83 | #10192 | semidirect |
| 337. M16 | #13050575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918770 | 2 |
| #24918378 | 2 |
| #24917915 | 2 |
| #24908390 | 2 |
| #24905957 | 2 |
| #24905314 | 2 |
| C83×#1980 | 2 |
| #10192 | 83 |