Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
600 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 115 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. C4×C4⋊#3633 | C2 | semidirect |
| 2. C4×C4⋊#3633 | C2 | semidirect |
| 3. C2×Q8⋊#3633 | C2 | semidirect |
| 53. C17×#124 | C8 | semidirect |
| 54. #10587633 | C8 | semidirect |
| 55. #10587622 | C8 | semidirect |
| 60. #10587561 | C8 | semidirect |
| 258. #124 | #3633 | semidirect |
| 289. C17 | #9675 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊#3633 | 2 |
| C2×Q8⋊#3633 | 2 |
| C2×D4⋊#3633 | 2 |
| #124×#595 | 2 |
| #9675 | 17 |