Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
372 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 88 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. #14545142 | C2 | semidirect |
| 2. #14544341 | C2 | semidirect |
| 3. #14543740 | C2 | semidirect |
| 4. #14543738 | C2 | semidirect |
| 70. Q16×C17 | M16 | semidirect |
| 73. D8×C17 | M16 | semidirect |
| 206. C17 | #11660 | semidirect |
| 219. Q16 | #63247 | semidirect |
| 222. D8 | #63247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545142 | 2 |
| #14544341 | 2 |
| #14543740 | 2 |
| #14543738 | 2 |
| #135×Dic17 | 2 |
| #11660 | 17 |