Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
800 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 116 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. C2×C4×C4⋊#595 | C2 | semidirect |
| 2. #14544676 | C2 | semidirect |
| 4. #14543657 | C2 | semidirect |
| 17. #11762711 | C4 | semidirect |
| 18. #11762710 | C4 | semidirect |
| 19. #11762705 | C4 | semidirect |
| 24. C17×#389 | C4 | semidirect |
| 249. #389 | #595 | semidirect |
| 312. C17 | #9148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C4⋊#595 | 2 |
| #14544676 | 2 |
| C2×#11763661 | 2 |
| #14543657 | 2 |
| #14537117 | 2 |
| #9148 | 17 |