Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1618 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1618 conjugacy classes of subgroups — too many to draw. Only its 331 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. C2×#11763198 | C2 | semidirect |
| 2. C2×#11763193 | C2 | semidirect |
| 3. C2×#11763186 | C2 | semidirect |
| 4. #14534890 | C2 | semidirect |
| 5. C17×#1726 | C2 | semidirect |
| 37. C17×#97 | D4 | semidirect |
| 38. C4×C8×C17 | D4 | semidirect |
| 84. #1726 | D17 | semidirect |
| 128. #97 | D68 | semidirect |
| 129. C4×C8 | D68 | semidirect |
| 131. C17 | #33308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763198 | 2 |
| C2×#11763193 | 2 |
| C2×#11763186 | 2 |
| #14534890 | 2 |
| C17×#1726 | 2 |
| #33308 | 17 |