Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
302 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 144 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. #14543701 | C2 | semidirect |
| 4. #14543700 | C2 | semidirect |
| 33. C16×D17 | C8 | semidirect |
| 49. C16×C17 | C2×C8 | semidirect |
| 50. #63214 | C2×C8 | semidirect |
| 93. D17 | #1313 | semidirect |
| 110. C17 | C2×#1313 | semidirect |
| 127. C16 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544985 | 2 |
| #14543978 | 2 |
| #14543701 | 2 |
| #14543700 | 2 |
| D17×#346 | 2 |
| C2×#1313 | 17 |