Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
290 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 130 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. #14543698 | C2 | semidirect |
| 4. #14543695 | C2 | semidirect |
| 59. C16×C17 | M16 | semidirect |
| 61. #63214 | M16 | semidirect |
| 135. C17 | #11408 | semidirect |
| 157. C16 | #63243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545144 | 2 |
| C8×#63243 | 2 |
| #14543698 | 2 |
| #14543695 | 2 |
| C4×C16×D17 | 2 |
| #11408 | 17 |