Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
538 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 90 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. #14545527 | C2 | semidirect |
| 2. #14544948 | C2 | semidirect |
| 3. #14544164 | C2 | semidirect |
| 4. #14544090 | C2 | semidirect |
| 5. #14543619 | C2 | semidirect |
| 6. #14543616 | C2 | semidirect |
| 24. #11763214 | C4 | semidirect |
| 25. #11763155 | C4 | semidirect |
| 26. #11763155 | C4 | semidirect |
| 30. C17×#493 | C4 | semidirect |
| 116. #63243 | D8 | semidirect |
| 220. #493 | #595 | semidirect |
| 293. C17 | #9053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545527 | 2 |
| #14544948 | 2 |
| #14544164 | 2 |
| #14544090 | 2 |
| #14543619 | 2 |
| #14543616 | 2 |
| #14539361 | 2 |
| #9053 | 17 |