Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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 |
|---|---|---|
| 3. #26013637 | C2 | semidirect |
| 5. #26013568 | C2 | semidirect |
| 6. #26013562 | C2 | semidirect |
| 7. #103×C349 | C2 | semidirect |
| 47. Dic349 | SD16 | semidirect |
| 52. C349 | #461 | semidirect |
| 60. #103 | D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150222 | 2 |
| C2×#19150220 | 2 |
| #26013637 | 2 |
| #26013601 | 2 |
| #26013568 | 2 |
| #26013562 | 2 |
| #103×C349 | 2 |
| #461 | 349 |