Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
814 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 179 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. C2×#11763251 | C2 | semidirect |
| 3. D17×#494 | C2 | semidirect |
| 4. #14531052 | C2 | semidirect |
| 5. #14531041 | C2 | semidirect |
| 6. #14531040 | C2 | semidirect |
| 7. #14531036 | C2 | semidirect |
| 8. C4×#10587469 | C2 | semidirect |
| 9. C17×#2247 | C2 | semidirect |
| 77. #10587469 | D4 | semidirect |
| 158. #2247 | D17 | semidirect |
| 167. C4×C17 | #510 | semidirect |
| 245. C17 | #33718 | semidirect |
| 328. C4 | #11763251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763251 | 2 |
| #14539213 | 2 |
| D17×#494 | 2 |
| #14531052 | 2 |
| #14531041 | 2 |
| #14531040 | 2 |
| #14531036 | 2 |
| C4×#10587469 | 2 |
| C17×#2247 | 2 |
| #33718 | 17 |