Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
510 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 147 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. C2×#11762586 | C2 | semidirect |
| 4. #14526864 | C2 | semidirect |
| 5. C17×#1375 | C2 | semidirect |
| 14. #11762588 | C4 | semidirect |
| 38. C2×C16×C17 | C2×C4 | semidirect |
| 44. C2×#63214 | C2×C4 | semidirect |
| 115. #1375 | D17 | semidirect |
| 124. C2×D17 | #347 | semidirect |
| 172. C2×C16 | C4×D17 | semidirect |
| 177. C17 | #12605 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#97×D17 | 2 |
| #14530394 | 2 |
| C2×#11762586 | 2 |
| #14526864 | 2 |
| C17×#1375 | 2 |
| #12605 | 17 |