Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
408 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 408 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×#11763733 | C2 | semidirect |
| 4. #14544889 | C2 | semidirect |
| 5. #14543858 | C2 | semidirect |
| 6. #14543824 | C2 | semidirect |
| 23. #11762613 | C4 | semidirect |
| 24. #11762611 | C4 | semidirect |
| 25. #11762609 | C4 | semidirect |
| 26. C17×#358 | C4 | semidirect |
| 90. Q16×C17 | C4⋊C4 | semidirect |
| 99. D136 | C4⋊C4 | semidirect |
| 180. #358 | #595 | semidirect |
| 227. C17 | #12955 | semidirect |
| 241. Q16 | C4⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763855 | 2 |
| C2×#11763733 | 2 |
| C2×#11763726 | 2 |
| #14544889 | 2 |
| #14543858 | 2 |
| #14543824 | 2 |
| #14530495 | 2 |
| #12955 | 17 |