Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
504 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 92 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. #14545013 | C2 | semidirect |
| 2. C2×#11763683 | C2 | semidirect |
| 3. #14543772 | C2 | semidirect |
| 4. #14543770 | C2 | semidirect |
| 14. #11763047 | C4 | semidirect |
| 16. #11763042 | C4 | semidirect |
| 20. #11762847 | C4 | semidirect |
| 22. C2×C17×#135 | C4 | semidirect |
| 31. C2×Q16×C17 | C2×C4 | semidirect |
| 33. C2×D8×C17 | C2×C4 | semidirect |
| 56. #10587489 | C2×C4 | semidirect |
| 57. #10587489 | C2×C4 | semidirect |
| 179. C2×#135 | #595 | semidirect |
| 208. C2×Q16 | C2×#595 | semidirect |
| 210. C2×D8 | C2×#595 | semidirect |
| 240. C17 | #11704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545013 | 2 |
| C2×#11763683 | 2 |
| #14543772 | 2 |
| #14543770 | 2 |
| #14538361 | 2 |
| #11704 | 17 |