Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 43 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×#10620284 | C2 | semidirect |
| 2. C2×D328 | C2 | semidirect |
| 3. C2×#10620282 | C2 | semidirect |
| 4. #13050160 | C2 | semidirect |
| 5. #13050153 | C2 | semidirect |
| 6. #13050074 | C2 | semidirect |
| 7. C2×SD16×C41 | C2 | semidirect |
| 36. C8×C41 | D4 | semidirect |
| 37. #66491 | D4 | semidirect |
| 55. C41 | #496 | semidirect |
| 57. C2×SD16 | D41 | semidirect |
| 92. C8 | C22⋊D41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10620284 | 2 |
| C2×D328 | 2 |
| C2×#10620282 | 2 |
| #13050160 | 2 |
| #13050153 | 2 |
| #13050074 | 2 |
| C2×SD16×C41 | 2 |
| #496 | 41 |