Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
594 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 86 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. #14544972 | C2 | semidirect |
| 4. #14544216 | C2 | semidirect |
| 5. #14543638 | C2 | semidirect |
| 6. #14543607 | C2 | semidirect |
| 22. #11763183 | C4 | semidirect |
| 23. #11763156 | C4 | semidirect |
| 24. #11763155 | C4 | semidirect |
| 28. C17×#492 | C4 | semidirect |
| 43. C17×C4⋊Q8 | C2×C4 | semidirect |
| 57. #10587555 | C2×C4 | semidirect |
| 67. C4×C8×C17 | C2×C4 | semidirect |
| 72. C4×#3622 | C2×C4 | semidirect |
| 110. C4×#595 | SD16 | semidirect |
| 220. #492 | #595 | semidirect |
| 252. C4⋊Q8 | C2×#595 | semidirect |
| 283. C4×C8 | C2×#595 | semidirect |
| 288. C17 | #9295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545276 | 2 |
| #14544972 | 2 |
| #14544292 | 2 |
| #14544216 | 2 |
| #14543638 | 2 |
| #14543607 | 2 |
| #14539721 | 2 |
| #9295 | 17 |