Finite Group DatabasebetaFinite Group DatabasebetaOrder 21568.
140 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 41 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×D2696 | C2 | semidirect |
| 2. C2×#19129170 | C2 | semidirect |
| 3. #24924955 | C2 | semidirect |
| 4. #24924921 | C2 | semidirect |
| 5. #24924888 | C2 | semidirect |
| 6. #24924879 | C2 | semidirect |
| 7. #102×C337 | C2 | semidirect |
| 26. D1348 | D4 | semidirect |
| 53. Dic337 | D8 | semidirect |
| 60. C337 | #459 | semidirect |
| 68. #102 | D337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D2696 | 2 |
| C2×#19129170 | 2 |
| #24924955 | 2 |
| #24924921 | 2 |
| #24924888 | 2 |
| #24924879 | 2 |
| #102×C337 | 2 |
| #459 | 337 |