Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
346 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 55. #10587495 | C8 | semidirect |
| 215. C17 | #9549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544337 | 2 |
| #14544088 | 2 |
| C2×#11763659 | 2 |
| M16×#3624 | 2 |
| #14543630 | 2 |
| #14543617 | 2 |
| #14528579 | 2 |
| #9549 | 17 |