Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
366 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 128 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. #11763736 | C4 | semidirect |
| 11. C16×#595 | C4 | semidirect |
| 15. #11762637 | C4 | semidirect |
| 16. #11762636 | C4 | semidirect |
| 17. C17×#367 | C4 | semidirect |
| 62. C16×C17 | C42 | semidirect |
| 63. #63214 | C42 | semidirect |
| 100. #595 | #367 | direct (N × H) |
| 116. #367 | #595 | direct (N × H) |
| 145. C17 | C4×#367 | semidirect |
| 170. C16 | C4×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763736 | 2 |
| C2×C16×#595 | 2 |
| #107×#595 | 2 |
| #14543841 | 2 |
| D17×#367 | 2 |
| C4×#367 | 17 |