Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
342 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 88 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×#11763740 | C2 | semidirect |
| 2. C2×#11763735 | C2 | semidirect |
| 3. #14543933 | C2 | direct (N × H) |
| 7. #11763740 | C22 | semidirect |
| 10. #11763735 | C22 | semidirect |
| 12. C2×D272 | C4 | semidirect |
| 16. D16×D17 | C4 | semidirect |
| 19. C2×C17×D16 | C4 | semidirect |
| 33. C17×D16 | C2×C4 | semidirect |
| 39. D272 | C2×C4 | semidirect |
| 127. C2×D16 | #595 | semidirect |
| 136. C2×C17 | #1415 | semidirect |
| 139. D17 | #1415 | semidirect |
| 157. D16 | C2×#595 | semidirect |
| 167. C17 | C2×#1415 | semidirect |
| 243. C2 | #14543933 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763740 | 2 |
| C2×#11763735 | 2 |
| #14543933 | 2 |
| C2×D16×D17 | 2 |
| C2×#1415 | 17 |