Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
866 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 866 conjugacy classes of subgroups — too many to draw. Only its 267 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×#11763207 | C2 | semidirect |
| 3. C2×#11763160 | C2 | semidirect |
| 5. #14528385 | C2 | direct (N × H) |
| 6. C2×C82×C17 | C2 | semidirect |
| 12. #11763207 | C22 | semidirect |
| 16. #11763160 | C22 | semidirect |
| 24. C82×C17 | C22 | semidirect |
| 115. C2×C82 | D17 | semidirect |
| 145. C82 | C2×D17 | semidirect |
| 146. C2×C17 | #1708 | semidirect |
| 179. C17 | C2×#1708 | semidirect |
| 248. C2 | #14528385 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763207 | 2 |
| C2×#11763182 | 2 |
| C2×#11763160 | 2 |
| C2×#11763156 | 2 |
| #14528385 | 2 |
| C2×C82×C17 | 2 |
| C2×#1708 | 17 |