Finite Group DatabasebetaFinite Group DatabasebetaOrder 21568.
268 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 268 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. #24925005 | C2 | semidirect |
| 2. #24924985 | C2 | semidirect |
| 3. #24924984 | C2 | semidirect |
| 4. #24924979 | C2 | semidirect |
| 5. C2×#19129170 | C2 | semidirect |
| 6. #24924966 | C2 | semidirect |
| 7. H(5,𝔽2)×C337 | C2 | semidirect |
| 9. #19129185 | C22 | semidirect |
| 10. C2×D1348 | C22 | semidirect |
| 12. #19129175 | C22 | semidirect |
| 13. #19129173 | C22 | semidirect |
| 14. #19129172 | C22 | semidirect |
| 15. #19129170 | C22 | semidirect |
| 16. #19129170 | C22 | semidirect |
| 17. #19129169 | C22 | semidirect |
| 18. C2×#14582106 | C22 | semidirect |
| 21. #41×C337 | C22 | semidirect |
| 23. C2×D4×C337 | C22 | semidirect |
| 54. C337 | #576 | semidirect |
| 57. H(5,𝔽2) | D337 | semidirect |
| 67. #41 | C2×D337 | semidirect |
| 71. C2×D4 | C2×D337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24925005 | 2 |
| #24924985 | 2 |
| #24924984 | 2 |
| #24924979 | 2 |
| C2×#19129170 | 2 |
| #24924966 | 2 |
| H(5,𝔽2)×C337 | 2 |
| #576 | 337 |