Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
398 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 228 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. C16×#3624 | C2 | semidirect |
| 23. #10587529 | C8 | semidirect |
| 30. C16×D17 | C8 | semidirect |
| 34. #63242 | C16 | direct (N × H) |
| 44. #63216 | C2×C8 | semidirect |
| 45. C16×C17 | C2×C8 | semidirect |
| 46. #63214 | C2×C8 | semidirect |
| 56. #3624 | C2×C16 | semidirect |
| 86. D17 | C8×C16 | semidirect |
| 102. C17 | C2×C8×C16 | semidirect |
| 118. C16 | #63242 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10587529 | 2 |
| C8×#63242 | 2 |
| C16×#3624 | 2 |
| C4×C16×D17 | 2 |
| C2×C8×C16 | 17 |