Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
496 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 496 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×#11763706 | C2 | semidirect |
| 2. C2×#11763677 | C2 | semidirect |
| 3. #14543754 | C2 | direct (N × H) |
| 8. #11763706 | C22 | semidirect |
| 10. #11763677 | C22 | semidirect |
| 15. #11763059 | C4 | semidirect |
| 17. C2×#10587488 | C4 | semidirect |
| 19. C22×D8×C17 | C4 | semidirect |
| 33. C2×D8×C17 | C2×C4 | semidirect |
| 54. #10587488 | C2×C4 | semidirect |
| 174. C22×D8 | #595 | semidirect |
| 192. C2×C17 | #1339 | semidirect |
| 202. C2×D8 | C2×#595 | semidirect |
| 231. C17 | C2×#1339 | semidirect |
| 351. C2 | #14543754 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763706 | 2 |
| C2×#11763677 | 2 |
| #14543754 | 2 |
| C2×#11763059 | 2 |
| C2×#1339 | 17 |