Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
842 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 842 conjugacy classes of subgroups — too many to draw. Only its 216 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 |
|---|---|---|
| 8. C4×C4⋊#595 | C4 | semidirect |
| 14. C2×#10587474 | C4 | semidirect |
| 15. C2×C8×Dic17 | C4 | semidirect |
| 16. C2×C17×#97 | C4 | semidirect |
| 63. C2×C8×C17 | C4⋊C4 | semidirect |
| 73. C2×#3622 | C4⋊C4 | semidirect |
| 123. Dic17 | H(3,ℤ/4) | semidirect |
| 131. C2×#97 | #595 | semidirect |
| 169. C17 | #10837 | semidirect |
| 191. C2×C8 | C4⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545233 | 2 |
| C2×#11763677 | 2 |
| C2×#11762761 | 2 |
| #10837 | 17 |