Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
438 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 3. #14544999 | C2 | semidirect |
| 4. #14544600 | C2 | semidirect |
| 5. #14543859 | C2 | semidirect |
| 6. #14543848 | C2 | semidirect |
| 10. #11763856 | C4 | semidirect |
| 11. #11763856 | C4 | semidirect |
| 12. #11763855 | C4 | semidirect |
| 13. #11763855 | C4 | semidirect |
| 21. #11763722 | C4 | semidirect |
| 22. #11763721 | C4 | semidirect |
| 29. #11762620 | C4 | semidirect |
| 30. #11762619 | C4 | semidirect |
| 31. #11762618 | C4 | semidirect |
| 32. C17×#360 | C4 | semidirect |
| 118. Q16×C17 | C42 | semidirect |
| 120. D8×C17 | C42 | semidirect |
| 130. Dic68 | C42 | semidirect |
| 131. D136 | C42 | semidirect |
| 229. #360 | #595 | semidirect |
| 291. C17 | #12650 | semidirect |
| 308. Q16 | C4×#595 | semidirect |
| 315. D8 | C4×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17⋊#444 | 2 |
| #14545092 | 2 |
| #14544999 | 2 |
| #14544600 | 2 |
| #14543859 | 2 |
| #14543848 | 2 |
| D17×#360 | 2 |
| #12650 | 17 |