Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
644 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 3. #14544896 | C2 | semidirect |
| 4. #14544895 | C2 | semidirect |
| 5. #14543618 | C2 | semidirect |
| 6. #14543618 | C2 | semidirect |
| 25. #11762553 | C4 | semidirect |
| 26. #11762552 | C4 | semidirect |
| 27. #11762552 | C4 | semidirect |
| 28. C17×#331 | C4 | semidirect |
| 65. C17×C4⋊C8 | C2×C4 | semidirect |
| 66. C17×C4⋊C8 | C2×C4 | semidirect |
| 69. C4⋊#3622 | C2×C4 | semidirect |
| 70. C4⋊#3622 | C2×C4 | semidirect |
| 258. #331 | #595 | semidirect |
| 303. C4⋊C8 | C2×#595 | semidirect |
| 304. C4⋊C8 | C2×#595 | semidirect |
| 310. C17 | #8921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545314 | 2 |
| #14544912 | 2 |
| #14544896 | 2 |
| #14544895 | 2 |
| #14543618 | 2 |
| D17×#331 | 2 |
| #8921 | 17 |