Finite Group DatabasebetaFinite Group DatabasebetaOrder 22976.
122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 2. C4×Dic718 | C2 | semidirect |
| 4. #26039947 | C2 | semidirect |
| 5. #26039940 | C2 | semidirect |
| 7. C4×C8×C359 | C2 | semidirect |
| 11. #19153330 | C4 | direct (N × H) |
| 22. Dic718 | C2×C4 | semidirect |
| 33. C8×C359 | C2×C4 | semidirect |
| 39. C4×C359 | SD16 | semidirect |
| 49. C359 | C4×SD16 | semidirect |
| 57. C4×C8 | D359 | semidirect |
| 83. C8 | C4×D359 | semidirect |
| 92. C4 | #19153330 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153330 | 2 |
| C4×Dic718 | 2 |
| C4×D1436 | 2 |
| #26039947 | 2 |
| #26039940 | 2 |
| #26039937 | 2 |
| C4×C8×C359 | 2 |
| C4×SD16 | 359 |