Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
246 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 78 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. #14544380 | C2 | semidirect |
| 2. #14543809 | C2 | semidirect |
| 3. #14543742 | C2 | semidirect |
| 4. #14543701 | C2 | semidirect |
| 23. C17×D16 | C8 | semidirect |
| 35. D8×C17 | C2×C8 | semidirect |
| 42. C16×C17 | C2×C8 | semidirect |
| 87. D16 | #3624 | semidirect |
| 97. C17 | #12067 | semidirect |
| 101. D8 | C2×#3624 | semidirect |
| 112. C16 | C2×#3624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544380 | 2 |
| #14543809 | 2 |
| #14543742 | 2 |
| #14543701 | 2 |
| #14530660 | 2 |
| #12067 | 17 |