Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
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×Dic698 | C2 | semidirect |
| 4. #26013571 | C2 | semidirect |
| 5. #26013564 | C2 | semidirect |
| 7. C4×C8×C349 | C2 | semidirect |
| 11. #19150222 | C4 | direct (N × H) |
| 22. Dic698 | C2×C4 | semidirect |
| 33. C8×C349 | C2×C4 | semidirect |
| 39. C4×C349 | SD16 | semidirect |
| 49. C349 | C4×SD16 | semidirect |
| 57. C4×C8 | D349 | semidirect |
| 83. C8 | C4×D349 | semidirect |
| 92. C4 | #19150222 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150222 | 2 |
| C4×Dic698 | 2 |
| C4×D1396 | 2 |
| #26013571 | 2 |
| #26013564 | 2 |
| #26013561 | 2 |
| C4×C8×C349 | 2 |
| C4×SD16 | 349 |