Finite Group DatabasebetaFinite Group DatabasebetaOrder 21568.
218 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 95 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. #24924954 | C2 | semidirect |
| 2. #24924949 | C2 | semidirect |
| 3. #24924944 | C2 | semidirect |
| 4. #24924942 | C2 | semidirect |
| 5. #24924938 | C2 | semidirect |
| 6. #24924937 | C2 | semidirect |
| 8. C4×C22⋊D337 | C2 | semidirect |
| 9. C2×C4⋊C4×C337 | C2 | semidirect |
| 66. C337 | #539 | semidirect |
| 76. C2×C4⋊C4 | D337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924954 | 2 |
| #24924949 | 2 |
| #24924944 | 2 |
| #24924942 | 2 |
| #24924938 | 2 |
| #24924937 | 2 |
| #24924933 | 2 |
| C4×C22⋊D337 | 2 |
| C2×C4⋊C4×C337 | 2 |
| #539 | 337 |