Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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. C2×C4×Dic353 | C2 | semidirect |
| 3. #26014918 | C2 | direct (N × H) |
| 4. C2×M16×C353 | C2 | semidirect |
| 7. #19150737 | C4 | semidirect |
| 9. C2×Dic706 | C4 | semidirect |
| 10. C2×D1412 | C4 | semidirect |
| 15. C4×Dic353 | C22 | semidirect |
| 18. M16×C353 | C22 | semidirect |
| 22. Dic706 | C2×C4 | semidirect |
| 24. D1412 | C2×C4 | semidirect |
| 54. C2×C353 | #104 | semidirect |
| 57. C353 | C2×#104 | semidirect |
| 60. C2×M16 | D353 | semidirect |
| 74. M16 | C2×D353 | semidirect |
| 113. C2 | #26014918 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150737 | 2 |
| C2×C4×Dic353 | 2 |
| #26014918 | 2 |
| C2×M16×C353 | 2 |
| C2×#104 | 353 |