Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
512 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 90 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. #14545243 | C2 | semidirect |
| 4. #14544113 | C2 | semidirect |
| 5. #14543681 | C2 | semidirect |
| 6. #14543611 | C2 | semidirect |
| 25. #11763095 | C4 | semidirect |
| 26. #11763094 | C4 | semidirect |
| 27. #11763006 | C4 | semidirect |
| 32. C17×#460 | C4 | semidirect |
| 119. C4×#595 | SD16 | semidirect |
| 235. #460 | #595 | semidirect |
| 310. C17 | #9238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545243 | 2 |
| #14544918 | 2 |
| #14544164 | 2 |
| #14544113 | 2 |
| #14543681 | 2 |
| #14543611 | 2 |
| #14538814 | 2 |
| #9238 | 17 |