Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1342 conjugacy classes of subgroups; only the 239 normal subgroups are shown.
This group has 1342 conjugacy classes of subgroups — too many to draw. Only its 239 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. D17×#493 | C2 | semidirect |
| 2. #14528399 | C2 | semidirect |
| 3. #14528398 | C2 | semidirect |
| 4. C82×D17 | C2 | semidirect |
| 5. C17×#1712 | C2 | semidirect |
| 8. #11763186 | C22 | semidirect |
| 9. #11763185 | C22 | semidirect |
| 12. C8×#3622 | C22 | semidirect |
| 13. C17×#493 | C22 | semidirect |
| 14. C82×C17 | C22 | semidirect |
| 41. C8×D17 | D8 | semidirect |
| 53. C8×C17 | C2×D8 | semidirect |
| 54. #3622 | C2×D8 | semidirect |
| 58. #1712 | D17 | direct (N × H) |
| 72. #493 | C2×D17 | semidirect |
| 75. C82 | C2×D17 | semidirect |
| 79. D17 | #1712 | direct (N × H) |
| 93. C17 | C2×#1712 | semidirect |
| 119. C8 | D8×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17×#493 | 2 |
| #14528399 | 2 |
| #14528398 | 2 |
| C82×D17 | 2 |
| C17×#1712 | 2 |
| C2×#1712 | 17 |