Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
662 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 127 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. C22×#10587499 | C2 | semidirect |
| 3. C2×#11762609 | C2 | semidirect |
| 4. #14526862 | C2 | semidirect |
| 5. C17×#1969 | C2 | semidirect |
| 26. C2×Q16×C17 | D4 | semidirect |
| 49. C2×#63214 | D4 | semidirect |
| 107. C2×C4×C17 | SD32 | semidirect |
| 125. #1969 | D17 | semidirect |
| 170. C2×Q16 | D68 | semidirect |
| 194. C17 | #13328 | semidirect |
| 256. C2×C4 | #10587499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587499 | 2 |
| C2×#11763186 | 2 |
| C2×#11762609 | 2 |
| #14526862 | 2 |
| C17×#1969 | 2 |
| #13328 | 17 |