Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
354 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 180 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. #14543695 | C2 | semidirect |
| 4. C16×#3624 | C2 | semidirect |
| 26. #10587530 | C8 | semidirect |
| 33. #10587469 | C8 | semidirect |
| 48. #63216 | C2×C8 | semidirect |
| 49. C16×C17 | C2×C8 | semidirect |
| 50. #63214 | C2×C8 | semidirect |
| 61. #3624 | M32 | semidirect |
| 110. C17 | C8×M32 | semidirect |
| 127. C16 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544991 | 2 |
| C8×#63242 | 2 |
| #14543695 | 2 |
| C16×#3624 | 2 |
| #14530377 | 2 |
| C8×M32 | 17 |