Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
306 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 306 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. #14543698 | C2 | semidirect |
| 4. C16×#3624 | C2 | semidirect |
| 40. #63247 | C16 | semidirect |
| 54. #63216 | M16 | semidirect |
| 70. #3624 | C2×C16 | semidirect |
| 126. C17 | C16×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763695 | 2 |
| C8×#63247 | 2 |
| #14543698 | 2 |
| C16×#3624 | 2 |
| #14530580 | 2 |
| C16×M16 | 17 |