Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
438 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 89 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. #14545951 | C2 | semidirect |
| 2. #14545817 | C2 | semidirect |
| 3. #14545805 | C2 | semidirect |
| 90. C23×C17 | M32 | semidirect |
| 95. C2×C4×C17 | M32 | semidirect |
| 188. C17 | #11466 | semidirect |
| 234. C23 | #10587670 | semidirect |
| 256. C2×C4 | #10587670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545951 | 2 |
| #14545817 | 2 |
| #14545805 | 2 |
| C2×D4×#3624 | 2 |
| #11466 | 17 |