Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
232 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 57 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×D2656 | C2 | semidirect |
| 2. C2×#19127536 | C2 | semidirect |
| 3. #24909711 | C2 | semidirect |
| 4. #24909309 | C2 | semidirect |
| 5. Dic83⋊C32 | C2 | semidirect |
| 6. #24905640 | C2 | semidirect |
| 7. C83×#1415 | C2 | semidirect |
| 29. D1328 | D4 | semidirect |
| 95. Dic83 | D32 | semidirect |
| 109. #1415 | D83 | semidirect |
| 110. C83 | #13685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D2656 | 2 |
| C2×#19127536 | 2 |
| #24909711 | 2 |
| #24909309 | 2 |
| Dic83⋊C32 | 2 |
| #24905640 | 2 |
| C83×#1415 | 2 |
| #13685 | 83 |