Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
230 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 230 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 |
|---|---|---|
| 2. #14545914 | C2 | semidirect |
| 3. #14545845 | C2 | semidirect |
| 4. #14545833 | C2 | semidirect |
| 6. #14545803 | C2 | semidirect |
| 42. C17×SD32 | C8 | semidirect |
| 43. #10587499 | C8 | semidirect |
| 44. #10587498 | C8 | semidirect |
| 45. #10587471 | C8 | semidirect |
| 63. Q16×C17 | C2×C8 | semidirect |
| 67. Dic68 | C2×C8 | semidirect |
| 71. C16×C17 | C2×C8 | semidirect |
| 72. #63214 | C2×C8 | semidirect |
| 144. SD32 | #3633 | semidirect |
| 160. C17 | #12065 | semidirect |
| 166. Q16 | C2×#3633 | semidirect |
| 186. 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 |
| #14545914 | 2 |
| #14545845 | 2 |
| #14545833 | 2 |
| #14545832 | 2 |
| #14545803 | 2 |
| #14545180 | 2 |
| #12065 | 17 |