Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
618 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14545926 | C2 | semidirect |
| 2. C42×#3633 | C2 | semidirect |
| 3. C2×Q8⋊#3633 | C2 | semidirect |
| 45. C17×#124 | C8 | semidirect |
| 46. #10587633 | C8 | semidirect |
| 47. #10587622 | C8 | semidirect |
| 50. #10587561 | C8 | semidirect |
| 201. #124 | #3633 | semidirect |
| 225. C17 | #9639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545926 | 2 |
| C42×#3633 | 2 |
| C2×Q8⋊#3633 | 2 |
| C2×D4⋊#3633 | 2 |
| #124×#595 | 2 |
| #9639 | 17 |