Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
578 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 92 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. #14545525 | C2 | semidirect |
| 2. #14544948 | C2 | semidirect |
| 3. C4×#10587547 | C2 | semidirect |
| 4. #14544130 | C2 | semidirect |
| 5. #14543681 | C2 | semidirect |
| 6. #14543615 | C2 | semidirect |
| 25. #11763090 | C4 | semidirect |
| 26. #11763089 | C4 | semidirect |
| 27. #11763001 | C4 | semidirect |
| 32. C17×#459 | C4 | semidirect |
| 129. #63243 | D8 | semidirect |
| 190. D68 | #104 | semidirect |
| 255. #459 | #595 | semidirect |
| 334. C17 | #8991 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545525 | 2 |
| #14544948 | 2 |
| C4×#10587547 | 2 |
| #14544130 | 2 |
| #14543681 | 2 |
| #14543615 | 2 |
| #14538783 | 2 |
| #8991 | 17 |