Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
948 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 112 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×#11763726 | C2 | semidirect |
| 2. C2×#11763725 | C2 | semidirect |
| 3. #14545012 | C2 | semidirect |
| 4. #14544660 | C2 | semidirect |
| 6. C2×#10587530 | C22 | semidirect |
| 7. C2×#10587533 | C22 | semidirect |
| 16. C2×#10587590 | C4 | semidirect |
| 22. C2×Q16×D17 | C4 | semidirect |
| 24. C2×D8×D17 | C4 | semidirect |
| 26. C2×C17×#135 | C4 | semidirect |
| 127. Q16×C17 | C22⋊C4 | semidirect |
| 130. D8×C17 | C22⋊C4 | semidirect |
| 143. Dic68 | C22⋊C4 | semidirect |
| 145. D136 | C22⋊C4 | semidirect |
| 229. C2×D17 | #360 | semidirect |
| 247. C2×#135 | #595 | semidirect |
| 322. C17 | #12735 | semidirect |
| 369. Q16 | C22⋊#595 | semidirect |
| 378. D8 | C22⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763726 | 2 |
| C2×#11763725 | 2 |
| #14545012 | 2 |
| #14544660 | 2 |
| C2×#135×D17 | 2 |
| #12735 | 17 |