Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
448 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 84 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. C2×#11763706 | C2 | semidirect |
| 2. C2×#11763677 | C2 | semidirect |
| 3. #14543756 | C2 | semidirect |
| 4. #14543754 | C2 | semidirect |
| 14. #11763064 | C4 | semidirect |
| 16. #11763059 | C4 | semidirect |
| 20. #11762847 | C4 | semidirect |
| 22. C2×C17×#135 | C4 | semidirect |
| 34. C2×Q16×C17 | C2×C4 | semidirect |
| 36. C2×D8×C17 | C2×C4 | semidirect |
| 62. #10587488 | C2×C4 | semidirect |
| 63. #10587488 | C2×C4 | semidirect |
| 191. C2×#135 | #595 | semidirect |
| 219. C2×Q16 | C2×#595 | semidirect |
| 221. C2×D8 | C2×#595 | semidirect |
| 256. C17 | #11685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763706 | 2 |
| C2×#11763677 | 2 |
| #14543756 | 2 |
| #14543754 | 2 |
| #14538389 | 2 |
| #11685 | 17 |