Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
954 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 264 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 |
|---|---|---|
| 7. #11763745 | C4 | semidirect |
| 8. C42×#595 | C4 | semidirect |
| 9. #11763677 | C4 | semidirect |
| 13. C2×#10587474 | C4 | semidirect |
| 14. C2×C8×Dic17 | C4 | semidirect |
| 15. C2×C17×#97 | C4 | semidirect |
| 56. C4×#595 | C42 | semidirect |
| 59. C2×C8×C17 | C42 | semidirect |
| 69. C2×#3622 | C42 | semidirect |
| 111. Dic17 | H(3,ℤ/4) | semidirect |
| 118. C2×#97 | #595 | semidirect |
| 152. C17 | C4×H(3,ℤ/4) | semidirect |
| 172. C2×C8 | C4×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10587677 | 2 |
| C2×#11763677 | 2 |
| C2×#11762761 | 2 |
| C4×H(3,ℤ/4) | 17 |