Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
170 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 50 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. C2×C4×#13083443 | C2 | semidirect |
| 3. #26015057 | C2 | semidirect |
| 4. #26015056 | C2 | semidirect |
| 7. #19150747 | C22 | semidirect |
| 11. C4×#13083443 | C22 | semidirect |
| 14. #19150737 | C4 | semidirect |
| 17. Q8×D353 | C4 | semidirect |
| 19. D4×D353 | C4 | semidirect |
| 22. #41×C353 | C4 | semidirect |
| 29. Dic706 | C2×C4 | semidirect |
| 31. D1412 | C2×C4 | semidirect |
| 44. Q8×C353 | C2×C4 | semidirect |
| 46. D4×C353 | C2×C4 | semidirect |
| 68. D353 | #104 | semidirect |
| 69. C353 | C2×#104 | semidirect |
| 81. #41 | #13083443 | semidirect |
| 97. Q8 | C2×#13083443 | semidirect |
| 104. D4 | C2×#13083443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D353⋊M16 | 2 |
| C2×C4×#13083443 | 2 |
| #26015057 | 2 |
| #26015056 | 2 |
| #41×D353 | 2 |
| C2×#104 | 353 |