Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
698 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 119 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×D272 | C2 | semidirect |
| 2. C22×#10587497 | C2 | semidirect |
| 3. C2×#11763184 | C2 | semidirect |
| 4. C2×#11762609 | C2 | semidirect |
| 5. #14529648 | C2 | semidirect |
| 6. #14526861 | C2 | semidirect |
| 7. C2×C17×#357 | C2 | semidirect |
| 60. C2×D136 | D4 | semidirect |
| 63. C2×C16×C17 | D4 | semidirect |
| 71. C2×#63214 | D4 | semidirect |
| 162. C2×Dic17 | D16 | semidirect |
| 180. C2×#357 | D17 | semidirect |
| 277. C2×C16 | C22⋊D17 | semidirect |
| 283. C17 | #13325 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D272 | 2 |
| C22×#10587497 | 2 |
| C2×#11763184 | 2 |
| C2×#11762609 | 2 |
| #14529648 | 2 |
| #14526861 | 2 |
| C2×C17×#357 | 2 |
| #13325 | 17 |