Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
2502 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2502 conjugacy classes of subgroups — too many to draw. Only its 667 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. C22×#10587562 | C2 | semidirect |
| 2. #14536858 | C2 | direct (N × H) |
| 3. C2×#11762739 | C2 | semidirect |
| 4. C2×#11762731 | C2 | semidirect |
| 6. C2×C17×#384 | C2 | semidirect |
| 9. C2×#10587562 | C22 | semidirect |
| 14. #11762739 | C22 | semidirect |
| 15. #11762731 | C22 | semidirect |
| 22. C17×#384 | C22 | semidirect |
| 34. C2×C42×C17 | D4 | semidirect |
| 69. C42×C17 | C2×D4 | semidirect |
| 104. C2×#384 | D17 | semidirect |
| 132. #384 | C2×D17 | semidirect |
| 135. C2×C17 | #2823 | semidirect |
| 160. C2×C42 | D68 | semidirect |
| 164. C17 | C2×#2823 | semidirect |
| 191. C42 | C2×D68 | semidirect |
| 231. C2 | #14536858 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587562 | 2 |
| #14536858 | 2 |
| C2×#11762739 | 2 |
| C2×#11762731 | 2 |
| C2×#11762726 | 2 |
| C2×C17×#384 | 2 |
| C2×#2823 | 17 |