Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
246 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 1. #14545915 | C2 | semidirect |
| 2. #14545845 | C2 | semidirect |
| 3. #14545832 | C2 | semidirect |
| 4. #14545804 | C2 | semidirect |
| 27. C17×D16 | C8 | semidirect |
| 28. #10587497 | C8 | semidirect |
| 29. D272 | C8 | semidirect |
| 41. D8×C17 | C2×C8 | semidirect |
| 43. D136 | C2×C8 | semidirect |
| 46. C16×C17 | C2×C8 | semidirect |
| 47. #63214 | C2×C8 | semidirect |
| 96. D16 | #3633 | semidirect |
| 106. C17 | #12067 | semidirect |
| 111. D8 | C2×#3633 | semidirect |
| 123. C16 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545915 | 2 |
| #14545845 | 2 |
| #14545832 | 2 |
| #14545804 | 2 |
| #14545182 | 2 |
| #12067 | 17 |