Finite Group DatabasebetaFinite Group DatabasebetaOrder 21568.
104 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 40 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. #24925047 | C2 | semidirect |
| 2. #24925046 | C2 | semidirect |
| 3. #24925030 | C2 | semidirect |
| 4. #24925024 | C2 | semidirect |
| 5. #24925023 | C2 | semidirect |
| 6. #24925013 | C2 | semidirect |
| 18. #19129175 | C4 | semidirect |
| 19. #19129174 | C4 | semidirect |
| 20. #19129170 | C4 | semidirect |
| 22. SD16×C337 | C4 | semidirect |
| 51. C337 | #444 | semidirect |
| 64. SD16 | #13062438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24925047 | 2 |
| #24925046 | 2 |
| #24925030 | 2 |
| #24925024 | 2 |
| #24925023 | 2 |
| #24925013 | 2 |
| #24924980 | 2 |
| #444 | 337 |