Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
202 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 202 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×C8×D353 | C2 | semidirect |
| 3. C4⋊C4×D353 | C2 | semidirect |
| 4. #26014914 | C2 | semidirect |
| 5. #26014913 | C2 | semidirect |
| 6. #26014912 | C2 | semidirect |
| 7. #102×C353 | C2 | semidirect |
| 12. D4×D353 | C4 | semidirect |
| 15. C2×#15667725 | C22 | semidirect |
| 17. C4⋊Dic353 | C22 | semidirect |
| 20. C2×C8×C353 | C22 | semidirect |
| 21. C4⋊C4×C353 | C22 | semidirect |
| 28. D1412 | C2×C4 | semidirect |
| 38. D4×C353 | C2×C4 | semidirect |
| 63. D353 | #102 | direct (N × H) |
| 64. C353 | C2×#102 | semidirect |
| 72. #102 | D353 | direct (N × H) |
| 83. C2×C8 | C2×D353 | semidirect |
| 86. C4⋊C4 | C2×D353 | semidirect |
| 97. D4 | C4×D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D353 | 2 |
| C2×C8×D353 | 2 |
| C4⋊C4×D353 | 2 |
| #26014914 | 2 |
| #26014913 | 2 |
| #26014912 | 2 |
| #102×C353 | 2 |
| C2×#102 | 353 |