Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
770 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 3. #14543728 | C2 | direct (N × H) |
| 34. C2×C22⋊C4×C17 | C8 | semidirect |
| 93. C22⋊C4×C17 | C2×C8 | semidirect |
| 216. C2×C17 | #1326 | semidirect |
| 243. C2×C22⋊C4 | #3624 | semidirect |
| 251. C17 | C2×#1326 | semidirect |
| 300. C22⋊C4 | C2×#3624 | semidirect |
| 397. C2 | #14543728 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763652 | 2 |
| #14543728 | 2 |
| C2×#11762684 | 2 |
| C2×#1326 | 17 |