Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
688 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 103 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. #14530455 | C2 | semidirect |
| 3. #14530433 | C2 | semidirect |
| 4. #14528754 | C2 | semidirect |
| 5. #14526912 | C2 | semidirect |
| 6. #14526904 | C2 | semidirect |
| 7. C17×#2883 | C2 | semidirect |
| 8. C2×#10587635 | C4 | semidirect |
| 9. C22×#63228 | C4 | semidirect |
| 17. #11762814 | C4 | semidirect |
| 18. #11762805 | C4 | semidirect |
| 44. C22×D68 | C2×C4 | semidirect |
| 63. #10587612 | C2×C4 | semidirect |
| 65. C2×#63223 | C2×C4 | semidirect |
| 66. C22×#3622 | C2×C4 | semidirect |
| 221. #2883 | D17 | semidirect |
| 342. C17 | #13102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14538052 | 2 |
| #14530455 | 2 |
| #14530433 | 2 |
| #14528754 | 2 |
| #14526912 | 2 |
| #14526904 | 2 |
| C17×#2883 | 2 |
| #13102 | 17 |