Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
346 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 67 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. #14541131 | C2 | semidirect |
| 2. #14530816 | C2 | semidirect |
| 3. #14528136 | C2 | semidirect |
| 4. #14526839 | C2 | semidirect |
| 5. #14526746 | C2 | semidirect |
| 6. #14526740 | C2 | semidirect |
| 7. C17×#2240 | C2 | semidirect |
| 109. D68 | D16 | semidirect |
| 121. #2240 | D17 | semidirect |
| 196. C17 | #12340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14541131 | 2 |
| #14530816 | 2 |
| #14528136 | 2 |
| #14526839 | 2 |
| #14526746 | 2 |
| #14526740 | 2 |
| C17×#2240 | 2 |
| #12340 | 17 |