Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
540 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 94 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. #14544960 | C2 | semidirect |
| 4. #14544134 | C2 | semidirect |
| 5. #14543681 | C2 | semidirect |
| 6. #14543615 | C2 | semidirect |
| 25. #11763100 | C4 | semidirect |
| 26. #11763099 | C4 | semidirect |
| 27. #11763011 | C4 | semidirect |
| 32. C17×#461 | C4 | semidirect |
| 120. #63243 | SD16 | semidirect |
| 239. #461 | #595 | semidirect |
| 315. C17 | #8989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#63243 | 2 |
| #14544960 | 2 |
| C4×#10587547 | 2 |
| #14544134 | 2 |
| #14543681 | 2 |
| #14543615 | 2 |
| #14538791 | 2 |
| #8989 | 17 |