Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
374 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 10. C4×#63214 | C4 | semidirect |
| 11. C16×Dic17 | C4 | semidirect |
| 12. C4×C16×C17 | C4 | semidirect |
| 45. C16×C17 | C4⋊C4 | semidirect |
| 46. #63214 | C4⋊C4 | semidirect |
| 72. C4×C17 | #367 | semidirect |
| 75. Dic17 | #367 | semidirect |
| 86. C4×C16 | #595 | semidirect |
| 106. C17 | #12906 | semidirect |
| 125. C16 | C4⋊#595 | semidirect |
| 150. C4 | #11763736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763736 | 2 |
| #14544720 | 2 |
| C4×C16×D17 | 2 |
| #12906 | 17 |