Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
322 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×Q8×D353 | C2 | semidirect |
| 3. #26014972 | C2 | semidirect |
| 4. #26014971 | C2 | semidirect |
| 5. #26014970 | C2 | semidirect |
| 6. #26014969 | C2 | semidirect |
| 7. #26014968 | C2 | semidirect |
| 8. C4⋊C4×D353 | C2 | semidirect |
| 9. C4⋊C4×D353 | C2 | semidirect |
| 11. C22⋊Q8×C353 | C2 | semidirect |
| 13. C2×Dic706 | C22 | semidirect |
| 14. C2×Dic706 | C22 | semidirect |
| 24. C4⋊Dic353 | C22 | semidirect |
| 25. C4⋊Dic353 | C22 | semidirect |
| 26. #19150716 | C22 | semidirect |
| 27. #19150716 | C22 | semidirect |
| 28. #19150716 | C22 | semidirect |
| 32. C2×Q8×C353 | C22 | semidirect |
| 34. C4⋊C4×C353 | C22 | semidirect |
| 35. C4⋊C4×C353 | C22 | semidirect |
| 39. C22×D353 | Q8 | semidirect |
| 64. C22×C353 | C2×Q8 | semidirect |
| 71. C2×D353 | C2×Q8 | semidirect |
| 86. D353 | C22⋊Q8 | direct (N × H) |
| 87. C353 | C2×C22⋊Q8 | semidirect |
| 96. C22⋊Q8 | D353 | direct (N × H) |
| 104. C2×Q8 | C2×D353 | semidirect |
| 119. C4⋊C4 | C2×D353 | semidirect |
| 120. C4⋊C4 | C2×D353 | semidirect |
| 159. C22 | Q8×D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D353 | 2 |
| C22×C4×D353 | 2 |
| #26014972 | 2 |
| #26014971 | 2 |
| #26014970 | 2 |
| #26014969 | 2 |
| #26014968 | 2 |
| C4⋊C4×D353 | 2 |
| C22⋊C4×D353 | 2 |
| C22⋊Q8×C353 | 2 |
| C2×C22⋊Q8 | 353 |