Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
444 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. #14543756 | C2 | direct (N × H) |
| 15. #11763064 | C4 | semidirect |
| 17. C2×#10587488 | C4 | semidirect |
| 19. C22×Q16×C17 | C4 | semidirect |
| 32. C2×Q16×C17 | C2×C4 | semidirect |
| 54. #10587488 | C2×C4 | semidirect |
| 165. C22×Q16 | #595 | semidirect |
| 182. C2×C17 | #1340 | semidirect |
| 191. C2×Q16 | C2×#595 | semidirect |
| 221. C17 | C2×#1340 | semidirect |
| 331. C2 | #14543756 | direct (N × H) |
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 |
| C2×#11763064 | 2 |
| C2×#1340 | 17 |