Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
720 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 107 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. #14545924 | C2 | semidirect |
| 2. C4×C22⋊#3633 | C2 | semidirect |
| 3. C2×#11763895 | C2 | semidirect |
| 56. C2×C22⋊C4×C17 | C8 | semidirect |
| 57. C2×C22⋊Dic17 | C8 | semidirect |
| 58. C2×#63227 | C8 | semidirect |
| 59. C2×#63227 | C8 | semidirect |
| 319. C2×C22⋊C4 | #3633 | semidirect |
| 335. C17 | #9651 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545924 | 2 |
| C4×C22⋊#3633 | 2 |
| C2×#11763895 | 2 |
| C2×#11763894 | 2 |
| C2×#11763759 | 2 |
| #9651 | 17 |