Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
914 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 251 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×#11763212 | C2 | semidirect |
| 4. #14528456 | C2 | direct (N × H) |
| 5. C2×#11762530 | C2 | semidirect |
| 6. C2×C17×#494 | C2 | semidirect |
| 11. #11763212 | C22 | semidirect |
| 19. #11762530 | C22 | semidirect |
| 23. C17×#494 | C22 | semidirect |
| 113. C2×#494 | D17 | semidirect |
| 138. #494 | C2×D17 | semidirect |
| 148. C2×C17 | #1722 | semidirect |
| 182. C17 | C2×#1722 | semidirect |
| 252. C2 | #14528456 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763212 | 2 |
| C2×#11763182 | 2 |
| C2×#11763157 | 2 |
| #14528456 | 2 |
| C2×#11762530 | 2 |
| C2×C17×#494 | 2 |
| C2×#1722 | 17 |