Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
750 conjugacy classes of subgroups; only the 397 normal subgroups are shown.
This group has 750 conjugacy classes of subgroups — too many to draw. Only its 397 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 |
|---|---|---|
| 6. C8×#3633 | C4 | direct (N × H) |
| 17. C4×#3633 | C8 | direct (N × H) |
| 21. C4×#3624 | C8 | semidirect |
| 22. C8×#595 | C8 | semidirect |
| 24. C4×C8×C17 | C8 | semidirect |
| 25. C8×Dic17 | C8 | semidirect |
| 26. C4×#3622 | C8 | semidirect |
| 52. #3633 | C4×C8 | direct (N × H) |
| 60. #3624 | C4×C8 | semidirect |
| 61. C8×C17 | C4×C8 | semidirect |
| 62. #3622 | C4×C8 | semidirect |
| 70. #595 | C82 | semidirect |
| 72. C4×C17 | C82 | semidirect |
| 74. Dic17 | C82 | semidirect |
| 102. C4×C8 | #3633 | direct (N × H) |
| 103. C17 | C4×C82 | semidirect |
| 138. C8 | C4×#3633 | direct (N × H) |
| 147. C4 | C8×#3633 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×#3633 | 2 |
| C2×C8×#3633 | 2 |
| C4×C8×#595 | 2 |
| C4×C82 | 17 |