Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
398 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 2. C2×#11763738 | C2 | semidirect |
| 4. #14544892 | C2 | semidirect |
| 5. #14543845 | C2 | semidirect |
| 6. #14543821 | C2 | semidirect |
| 23. #11762614 | C4 | semidirect |
| 24. #11762612 | C4 | semidirect |
| 25. #11762610 | C4 | semidirect |
| 26. C17×#357 | C4 | semidirect |
| 178. #357 | #595 | semidirect |
| 223. C17 | #12939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763851 | 2 |
| C2×#11763738 | 2 |
| C2×#11763723 | 2 |
| #14544892 | 2 |
| #14543845 | 2 |
| #14543821 | 2 |
| #14530488 | 2 |
| #12939 | 17 |