Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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×#10587498 | C2 | semidirect |
| 2. C2×#11763085 | C2 | semidirect |
| 4. #14530505 | C2 | semidirect |
| 5. C2×#11762594 | C2 | semidirect |
| 6. #14526881 | C2 | semidirect |
| 7. C2×C17×#361 | C2 | semidirect |
| 54. C2×Dic68 | D4 | semidirect |
| 66. C17×#108 | D4 | semidirect |
| 74. C2×#63214 | D4 | semidirect |
| 175. C2×#361 | D17 | semidirect |
| 264. #108 | C22⋊D17 | semidirect |
| 269. C17 | #13321 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587498 | 2 |
| C2×#11763085 | 2 |
| #14538428 | 2 |
| #14530505 | 2 |
| C2×#11762594 | 2 |
| #14526881 | 2 |
| C2×C17×#361 | 2 |
| #13321 | 17 |