Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
604 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 96 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. C4×Q8×#595 | C2 | semidirect |
| 4. #14544113 | C2 | semidirect |
| 5. #14543681 | C2 | semidirect |
| 6. #14543611 | C2 | semidirect |
| 25. #11763091 | C4 | semidirect |
| 26. #11763010 | C4 | semidirect |
| 27. #11763009 | C4 | semidirect |
| 32. C17×#475 | C4 | semidirect |
| 123. C4×#595 | SD16 | semidirect |
| 164. Q8×C17 | #104 | semidirect |
| 196. Dic34 | #104 | semidirect |
| 238. #475 | #595 | semidirect |
| 316. C17 | #9234 | semidirect |
| 389. Q8 | #10587550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×#595 | 2 |
| #14544917 | 2 |
| #14544165 | 2 |
| #14544113 | 2 |
| #14543681 | 2 |
| #14543611 | 2 |
| #14538817 | 2 |
| #9234 | 17 |