Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
802 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 111 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. #24908298 | C2 | semidirect |
| 3. #24907407 | C2 | semidirect |
| 4. #24905978 | C2 | semidirect |
| 5. #24905369 | C2 | semidirect |
| 6. #24905349 | C2 | semidirect |
| 7. C83×#2339 | C2 | semidirect |
| 8. C2×#14581817 | C4 | semidirect |
| 14. #19127702 | C4 | semidirect |
| 29. C22×D332 | C2×C4 | semidirect |
| 35. C2×#13050574 | C2×C4 | semidirect |
| 40. C2×C4⋊Dic83 | C2×C4 | semidirect |
| 160. D4×C83 | #99 | semidirect |
| 240. #2339 | D83 | semidirect |
| 246. C83 | #9365 | semidirect |
| 404. D4 | #14581706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916715 | 2 |
| #24908298 | 2 |
| #24907407 | 2 |
| #24905978 | 2 |
| #24905369 | 2 |
| #24905349 | 2 |
| C83×#2339 | 2 |
| #9365 | 83 |