Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
814 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 199 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. #14531037 | C2 | semidirect |
| 4. #14531036 | C2 | semidirect |
| 5. #14531035 | C2 | semidirect |
| 7. C17×#2247 | C2 | semidirect |
| 91. C4×D17 | Q32 | semidirect |
| 106. #2247 | D17 | direct (N × H) |
| 112. C4×C17 | C2×Q32 | semidirect |
| 117. Dic17 | C2×Q32 | semidirect |
| 137. D17 | #2247 | direct (N × H) |
| 165. C17 | C2×#2247 | semidirect |
| 221. C4 | Q32×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q32×D17 | 2 |
| D17×#494 | 2 |
| #14531037 | 2 |
| #14531036 | 2 |
| #14531035 | 2 |
| C4×C16×D17 | 2 |
| C17×#2247 | 2 |
| C2×#2247 | 17 |