Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
578 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 112 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. C22×#10587529 | C2 | semidirect |
| 2. C2×#11763721 | C2 | semidirect |
| 3. #14544661 | C2 | semidirect |
| 4. #14543841 | C2 | semidirect |
| 17. #11763046 | C4 | semidirect |
| 18. #11763045 | C4 | semidirect |
| 21. #11763042 | C4 | semidirect |
| 24. C17×#466 | C4 | semidirect |
| 58. #10587529 | D4 | semidirect |
| 175. C22×C17 | #357 | semidirect |
| 186. C2×D17 | #357 | semidirect |
| 211. #466 | #595 | semidirect |
| 268. C17 | #13059 | semidirect |
| 386. C22 | #11763721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587529 | 2 |
| C2×#11763721 | 2 |
| #14544661 | 2 |
| #14543841 | 2 |
| D17×#466 | 2 |
| #13059 | 17 |