Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
806 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 195 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. C22×D272 | C2 | semidirect |
| 2. C22×C16×D17 | C2 | semidirect |
| 3. C2×#11763046 | C2 | semidirect |
| 4. #14530871 | C2 | direct (N × H) |
| 5. C2×#11762609 | C2 | semidirect |
| 6. C2×C17×#366 | C2 | semidirect |
| 11. C2×D272 | C22 | semidirect |
| 14. C2×C16×D17 | C22 | semidirect |
| 16. #11763046 | C22 | semidirect |
| 18. #11762609 | C22 | semidirect |
| 21. C17×#366 | C22 | semidirect |
| 39. C2×C16×C17 | D4 | semidirect |
| 78. C16×C17 | C2×D4 | semidirect |
| 88. C22×D17 | D16 | semidirect |
| 113. C2×#366 | D17 | semidirect |
| 126. C2×D17 | C2×D16 | semidirect |
| 145. #366 | C2×D17 | semidirect |
| 147. C2×C17 | #2215 | semidirect |
| 174. C2×C16 | D68 | semidirect |
| 179. C17 | C2×#2215 | semidirect |
| 211. C16 | C2×D68 | semidirect |
| 259. C2 | #14530871 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D272 | 2 |
| C22×C16×D17 | 2 |
| C2×#11763046 | 2 |
| #14530871 | 2 |
| C2×#11762609 | 2 |
| C2×C17×#366 | 2 |
| C2×#2215 | 17 |