Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
154 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 48 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. D353⋊M16 | C2 | semidirect |
| 2. #26015071 | C2 | semidirect |
| 3. #26015057 | C2 | semidirect |
| 5. #19150747 | C22 | semidirect |
| 10. C4×#13083443 | C22 | semidirect |
| 13. #19150738 | C4 | semidirect |
| 16. C2×D1412 | C4 | semidirect |
| 19. C2×Q8×C353 | C4 | semidirect |
| 56. C353 | #421 | semidirect |
| 66. C2×Q8 | #13083443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D353⋊M16 | 2 |
| #26015071 | 2 |
| #26015057 | 2 |
| C2×#19150738 | 2 |
| #421 | 353 |