Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
822 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 155 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. #14529711 | C2 | semidirect |
| 3. C2×#11762553 | C2 | semidirect |
| 4. #14526625 | C2 | semidirect |
| 5. C17×#2366 | C2 | semidirect |
| 9. #11763185 | C4 | semidirect |
| 43. #10587560 | C2×C4 | semidirect |
| 50. C4×#3622 | C2×C4 | semidirect |
| 82. C4⋊C4×C17 | D8 | semidirect |
| 141. #2366 | D17 | semidirect |
| 220. C17 | #9061 | semidirect |
| 259. C4⋊C4 | #63228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763185 | 2 |
| #14529711 | 2 |
| C2×#11762553 | 2 |
| #14526625 | 2 |
| C17×#2366 | 2 |
| #9061 | 17 |