Finite Group DatabasebetaFinite Group DatabasebetaOrder 21568.
124 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 46 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×#19129195 | C2 | semidirect |
| 2. C2×#19129193 | C2 | semidirect |
| 3. #24925026 | C2 | semidirect |
| 4. #24925016 | C2 | semidirect |
| 5. #24925016 | C2 | semidirect |
| 6. #24925014 | C2 | semidirect |
| 24. #14582113 | D4 | semidirect |
| 43. C2×D337 | M16 | semidirect |
| 55. C337 | #435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19129195 | 2 |
| C2×#19129193 | 2 |
| #24925026 | 2 |
| #24925016 | 2 |
| #24925014 | 2 |
| #24924921 | 2 |
| #435 | 337 |