Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
306 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 91 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. #14531057 | C2 | semidirect |
| 3. #14531009 | C2 | semidirect |
| 4. #14531007 | C2 | semidirect |
| 5. #14528376 | C2 | semidirect |
| 6. C8×#63214 | C2 | semidirect |
| 7. C17×#1706 | C2 | semidirect |
| 69. #63214 | SD16 | semidirect |
| 89. C8×C17 | D16 | semidirect |
| 97. #1706 | D17 | semidirect |
| 154. C17 | #12503 | semidirect |
| 198. C8 | #10587497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14531057 | 2 |
| #14531033 | 2 |
| #14531009 | 2 |
| #14531007 | 2 |
| #14528376 | 2 |
| C8×#63214 | 2 |
| C17×#1706 | 2 |
| #12503 | 17 |