Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
378 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 100 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. #14544337 | C2 | semidirect |
| 4. M16×#3624 | C2 | semidirect |
| 5. #14543630 | C2 | semidirect |
| 6. #14543617 | C2 | semidirect |
| 55. #10587504 | C8 | semidirect |
| 227. C17 | #9550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544337 | 2 |
| #14544083 | 2 |
| C2×D4⋊#3624 | 2 |
| M16×#3624 | 2 |
| #14543630 | 2 |
| #14543617 | 2 |
| #100×Dic17 | 2 |
| #9550 | 17 |